Let's Do Mathematics 4 – Worktext B

n ca t Wo r k t e xt x

4B

for le arne arners 9 - 10 year s o l d

2 km 25 min hike

Let’s Do Mathematics

Re ga le du ca tio n

Let’s Do Mathematics is a series covering levels K-6 and is fully aligned to o the United States Common Core State Standards (USCCSS). Each level consists of two books boo (Book A and Book B) and combines textbook-style presentation of concepts oncepts pts as well as workbook practice.

Central to the USCCSS is the promotion of problem-solving skills ls and reasoning.

Let’s Do Mathematics achieves this by teaching and presenting ng g concepts through throu a problem-solving based pedagogy and using the concrete-pictorial-abstract pictorial-abstract torial-abstract ((CPA) approach. Learners acquire knowledge and understanding a ng off concepts through thr th guided progression beginning with concrete examples and experiences which then w flow into pictorial representations and finally mastery at the and symbolic level. e abstract an a This approach ensures that learners develop a fundamental understanding of concepts damental ental understa underst rather than answering questions by learned procedures edures es and algorithms. algorit

Key features of the series include:

Anchor Task

9

Graphs Line Plots and Line G

Length of Pencils Total Tally

Length

Anchor Task

Open-ended activities serve as the starting point for understanding new vities concepts. Learners engage in activities e and discussions to form concrete experiences before the conceptt is formalized.

20 209

0 208

Let’s Learn n

Concepts are presented sented in a clear and a colorful manner.. Worked rked problems problem provide learners step-by-step ers with ith guided step-by ste progression through Series gh examples. Ser mascots provide rovide de guidance through throug throu helpful comments observations omments ments and observa when new concepts oncepts are introduced. intro

Numbers to Let’s Learn

Count on in

+1,000

5,000

1,000,000

thousands

6,000

Find the num ber represen ted in the plac e value cha

from 5,000.

+1,000

(a)

+1,000

7,000

Ten Thousands Thousand s

+1,000

8,000

1,000 more than 9,000 is 10,0 We read 10,0 00 as ten thou 00. sand. ten thousand s from 50,0 00.

We say: We write:

10,000

(b)

Count on in

+10,000

50,000

+10,000

60,000

+10,000

70,000

+10,000

80,000

500,000

+100,000

600,000

+100,000

700,000

800,000

100,000 mor e than 900 ,000 We read 1,00 0,000 as one is 1,000,000. million.

4

Ones

Hundreds

Tens

Ones

+10,000

We say:

90,000

+100,000

Tens

Twenty-five thousand, one 25,170. hundred seve nty.

Hundred Ten Thousands Thousands Thousand s

10,000 mor e than 90,0 00 is 100,000 We read 100, .

000 as one hundred thou sand.

Count on in one hundred thousands from 500,000 . +100,000

rt.

Hundreds

+1,000

9,000

100,000

We write:

Three hundred hundred thirt forty-two thousand, eight y-three.

342,833.

(c)

Hundred Ten Thousands Thousands Thousand s

We say: We write:

+100,000

900,000

1,000,000

(d)

Hundred Ten Thousands Thousands Thousand s

We say: We write:

Hundreds

Tens

Ones

Five hundred one thousand 501,062. , sixty-two.

Hundreds

Tens

Nine hundred thirty thousand 930,107. , one hundred

Ones

seven.

5

ii

Let’s Practice

2.

Let’s Practice 1.

Write

time using a.m. and

p.m.

(b)

(a)

(b)

(a)

Learners demonstrate their understanding of concepts through a range of exercises and problems to be completed in a classroom environment.

Questions provide a varying degree of guidance and scaffolding as learners progress to mastery of the concepts.

Write the times in 12-hour

time. the times in 24-hour

15 15 1:15

0 3:30

(d))

(c)

Morning:

Re ga le du ca tio n

Morning:

(f)

(e)

Afternoon:

Afternoon:

(d)

(c)

5 1:::5 11:5 11:50 111:

:2 9:25 9

t the table. ete Comple

3.

t International Airpor Flight Departures JFK Departure Departure (24-hour time) (12-hour)

Morning:

Morning:

City

Night:

Night:

1:45 a.m.

less Los Angele

(f)

(e)

07 35

Miamii

0 9:05 9

5 45 4 :4 :45 7:4 77:45

3:40 p.m.

Dallas

g: Morn Morning

i g: Mornin

0 20 20

g gton Wa Washin Was

23

Night:

(b) Home At

1.

Write the equivalent

2.

fractions.

Use multiplication

(a)

(a)

At Home

to find equivalent

x2

4 7

x2

1 2

=

=

(b) (b

(b)

x2

2 9

Further practice designed to be completed without the guidance of a teacher. Exercises and problems in this section follow on from those completed under Let’s Practice.

x3

2 9

=

x2

1 3

=

=

3.

=

Use division to find

(a) (a

3 4

=

(b)

3 6

÷6

18 42

=

÷3

=

18 = 42

152

=

=

÷3

18 42

=

÷4

÷4

12 = 20

(d)

equivalent fractio ns.

12 20

=

÷2

=

=

x4

=

÷2

12 20

x4

2 9

=

x3

2 = 9

(c)

=

x3

4 = 7

=

fractions.

x3

4 7

=

=

÷6

=

153

Hands On

Learners are encouraged to ‘learn by doing’ through the use of group activities and the use of mathematical manipulatives.

d . he dice n on the hown how Hands On err ssh ber mbe umb um num ets. ke kets ket he n h e the Mov Move i e. Mo ice shown in brac g a dice ng ing ling rollin i ro nt to the unit ent u ns in eme ake ttur a Take measurem cm ic m trric met e me rt the ert er v vert ver nve Con

36 cm (mm)

22,000 g (kg)

start. es back to the me rules: Som S rrectly,, go 3 spaces. a wer inco leap forward • If you ans a honey pot, 3 spaces. k ou land on • If you a bee, fly bac you land on • Iff y winner! hive is the h bee e the to er The first play

11 km (m)

182 dm (cm)

ST RT STA

0 cm 110 dm)) ((dm (d

7 kg (g)

4,000 m (km (km)

0 ml 000 00 ,000 6,00 6 (l)

14 kg (g)

Solve It!

5l (ml)

Solve It!

What is Sophie’s favorite fruit?

Match the mixed numbe rs and improper fractions to find out.

10 km (m)

N

FINISH

R

0 80

Activities that require learners earners ers to apply logical reasoning problem-solving. Problems ng and nd problem-solvin problem-s hich do o not have a rou are often posed which routine strategy rners are encouraged encourag enc for solving them. Learners to think creatively and apply problem-solving y a range of probl p heuristics.

M

D

22 3

Consolidated solidated practice where whe learners demonstrate on a emonstrate their understanding under u range ange of concepts taught taug within a unit.

4

7

1 = 8

=

(e)

3 = 7

=

=

(f)

2 = 9

=

15

4

(d)

12 = 16

(e)

18 = 36

(f)

15 = 45

9 8

(d)

21

4

5 2

12 5

Write the improper fraction represented of the shapes.

by the colored parts

5.

Write the mixed number represented the shapes in its simplest form.

by the colored parts of

(a)

(b)

on 6. Draw a point to show the fraction

the number line.

1

(a) 2 3

by writing = or ≠.

3. Tell whether the fractions are equivalent (b) 12 2 (a) 6

3 4

4 3

(b)

2 = 5

5 = 20

(c)

7 4

5

(a)

(d)

(c)

9

12

=

form.

2. Find the equivalent fraction in its simplest (b) 9 (a) 2 = =

1 3

4 3

4.

4

1. Find the first 2 equivalent fractions. (b) 3 (a) 1 = = =

(c)

I

166

Looking Back

Looking Back

A

14

7

11 33

1 3

0

2

1

3

9

(b) 6

0

1

2

221

220

iii

Contents 2 2 20 25 34

Re ga le du ca tio n 5 Time Converting Units of Time Expressing 12-hour and 24-hour Time Duration of Time Word Problems a 6 Measurement, Perimeter and Area zes Benchmarks and Relative Sizes Converting Customary Units its Converting Metric Units Perimeter Area Word Problems

42 43 58 72 84 100 120

Angles Identifying and nd Naming ming Angles A g Angles Angle g Comparing g Angles Measuring Drawing g Angles ngles Properties erties es of Angles Ang rd Problems roblems Word

134 135 140 150 160 170 179

7

8 Symmetry mmetry Identifying Sym Symmetric Figures Drawing Sym Symmetric Figures 6

iv

190 192 200

208 210 230

10 Problem Solving Act It Out Draw a Model Guess-and-Check Make a List Look for Patterns Work Backwards Before-After Concept Simplify the Problem

248 248 253 258 263 268 274 278 282

tio n

9 Line Plots and Line Graphs Interpreting and Creating Line Plots Interpreting and Creating Line Graphs

v

Time

Converting Units of Time

Re ga

Anchor Task

Activity

2

Time (s)

tio n

5

Time (min and s)

Let’s Learn

ati on

and and The analog clock below has an hour hand, minute hand second hand.

hour hand

second hand

e

minute hand

The hour hand moves oves ves the th t slowest. we It takes the hour hand one hour to move from to the next. It takes the hour hand m one ne number numb num 12 hours to move ve once around aroun the t clock. There are 24 hours in one day. So, the hour ourr hand moves mov around the clock 2 times in one day.

The minute than the hour hand. It takes the te hand an moves move faster f minute hand nd 5 minutes to move from one number to the next.

It takes es the e minute hand han 60 minutes, or one hour, to move once around und the clock. There The are 60 minutes in one hour. moves the fastest. It takes the second hand The second hand h 5 seconds from one number to the next. It takes the econds to move econd m second hand ha 60 seconds, or one minute, to move once around the clock. There are 60 seconds in one minute. h 3

Re ga le du ca tio n

We know that in 1 minute there are 60 seconds.

How many seconds are there in 2 minutes?

2 min = 2 x 60 s = 120 s

There are 120 s in 2 min.

1 min 2 min 3 min 4 min 5 min

= 60 s = 120 s = 180 s = 240 s = 300 s

Use this chart een to convert between minutes and seconds. secon

n 3 min 13 s.

Blake finished a running race in s.

Express the time in seconds.

3 min 13 s

0s 3 min = 180 13 s

3s 3 min 13 s = 180 s + 13 = 193 s

d the e running race r Blake finished in 193 seconds.

5 seconds in minutes m Expresss 255 and seconds.

255 s = 240 s + 15 s 1 s = 4 min 15

4

Re ga le du ca tio n

We know that in 1 hour there are 60 minutes.

How many minutes are there in 4 hours?

4 h = 4 x 60 min = 240 min

There are 240 min in 4 hours.

1 h = 60 min 2 h = 120 min 3 h = 180 min 4 h = 240 min 5 h = 300 min

Use this chart een to convert between utes. hours and minutes.

5 min.

Sophie went on a hike for 4 h 35 d in minutes. minute minut Express the time Sophie hiked 4 h 35 min

0 min 4 h = 240 35 min

0 min + 35 min m 4 h 35 min = 240 = 275 min ed for 275 min. min Sophie hiked

ess ss 282 minutes minu Express in hours and minutes.

282 82 min = 240 min + 42 min = 4 h 42 s

5

Let’s Practice Convert the times to seconds.

Re ga le du ca tio n

1.

onds. (a) Riley talked on the phone for 2 minutes 21 seconds. econds? nds How long did Riley talk on the phone in seconds? min =

2 min 21 s

s

s

2 min 21 s =

s+

=

s

s

one e for Riley talked on the phone

seconds.

(b) Wyatt heated his dinner minutes 47 seconds. ner for 3 m How long did Wyatt dinner for in seconds? yattt heat his d min =

3 min 47 s

s

s

3 min 47 s =

=

s+ s

Wyatt he heated his dinner for

6

s

seconds.

Re ga le du ca ti n

(c) Halle sang a song for 4 minutes 12 seconds.

How long did Halle sing for in seconds? min =

4 min 12 s

s

s

4 min 12 s = =

s+

s

s

seconds. ds.

Halle sang for

(d) A news update lasted 3 minutes nutes 38 seconds. se s wss update in seconds? se How long was the news min =

3 min 38 s

s

s

3 min 38 s =

=

s+ s

e news ews update we The went for

2.

s

seconds. d

Write te the he time in sec seconds. (a) a)) 3 min 18 s =

s

(b) 1 min 50 s =

s

(c) 4 min 4 42 s =

s

(d) 2 min 46 s =

s

min 2 (e)) 1 m 23 s =

s

(f) 4 min 17 s

s

=

7

3.

Convert the times to minutes and seconds. conds. (a) Chelsea danced for 95 seconds.

How long did Chelsea dance for in minutes and seconds?

95 s =

s+

=

s

Re ga le du ca t

min

s

min

Chelsea danced for

s s.

(b) A train takes 124 seconds to travel from one stop to the e next. ext.

How long does the train take ke in minutes and seconds??

124 s =

=

s+

s

min

akes kes The train takes

s

min m

s.

(c) Sophie ran 1 km in 265 26 sseconds. ong g did she take ta to run How long 1 km m in minutes minut minu es and a seconds? s 265 5s=

=

s+

min

Sophie Sophie ran ra 1 km in

8

s

s

min

ss.

(d) Ethan completed a mathematics quiz in 410 seconds. How long did it take Ethan to finish the quiz in minutes and seconds?

410 s =

s

min

s

Re ga le du ca t

=

s+

min

Ethan completed the quiz in

s.

e (e) It took Halle 278 seconds to make her bed. How long did it take ke herr in minutes and seconds?

278 s =

=

s+

min n

s

s

Halle made her bed d in

4.

min

s.

n minutes minu min Write the time in and seconds. (a) 68 s =

min

s

(b) 101 s =

mi min

s

(c) 317 s =

min m mi

s

(d) d) 299 99 s =

min

s

(e)) 138 s =

min

s

9

5.

Convert the times to minutes. tes. (a) Jordan took a nap for 2 hours 15 minutes.

How long did Jordan nap in minutes? h=

min

Re ga le du ca tio

2 h 15 min

min

2 h 15 min =

min +

min n

min

=

Jordan took a nap for

minutes.

orr 3 hours 46 minutes. m (b) Wyatt played tennis for y tennis for in minutes?

How long did Wyatt play h=

3 h 46 min

min

min

3 h 46 min n =

=

min + min m

Wyatt played tennis te for

10

min

minutes. s.

Re ga le du ca tio n

(c) Mrs. Lee worked in her garden for 4 hours 21 minutes.

How long did Mrs. Lee work in her garden in minutes? nutes? es? min =

4 h 21 min

min n

min

4 h 21 min =

=

min +

min n

min

en for or Mrs. Lee worked in her garden

minutes. m

(d) Riley watched a movie that 7 minutes. at went ent for 2 hours h How long was the movie e in minutes? min =

2 h 7 min

min

min

2 h 7 min =

=

min + min m mi

vie was The movie

6.

min

minutes long.

Write the time in minu minutes. mi (a) 3 h 8 min =

min

(b) 3 h 33 min =

min

(c) 1 h 45 mi min =

min

(d) 4 h 15 min =

min

(f) 2 h 56 min =

min

min = (e) 4 h 28 m

min

11

7.

Convert the times to hours and minutes. es. (a) A car ride to the beach takes 95 minutes.

How long is the trip in hours and minutes? es?

95 min =

min

Re ga le du ca tio

min + h

=

min

The car ride to the beach takes

h

eattle le (b) A flight from Los Angles to Seattle ng does oes takes 192 minutes. How long nd minutes? minutess? the flight take in hours and 192 min =

min n+

min mi n

h

=

The flight takes kes

min

h

min.

ayed ed golf for 425 minutes. (c) Blake played ong did Blake play golf for in How long rs and minutes? minute hours 425 5 min =

=

min + h

Bl k pla Blake played golf for

12

min n

min h

min.

min.

(d) Chelsea read a book for 152 minutes.

How long did she read for in hours and minutes?

152 min =

min

Re ga le du ca tio

min +

=

h

min

h

Chelsea read for

min. n.

o milk (e) Mr. Jones took 395 minutes to d he e all of his cows. How long did take in hours and minutes? es?

395 min = =

min in + h

min m

min mi

k alll of his c Mr. Jones milked cows in

8.

h

min.

Write the time and me in n hours an a minutes. (a) 168 min n =

h

min

(b) 109 9 min n=

h

min

(c) c) 377 77 min =

h

min

((d) 218 min =

h

min

(e)) 40 min = 405 m

h

min

13

Solve It!

1.

tio n

Complete each table to help find the answer.

conds. ds.

Sophie finished a mathematics quiz in 222 seconds. second Riley finished the same quiz in 3 minutes 40 seconds.

Who finished the mathematics quiz in the shorter time?

Minutes

Seconds

1

Re ga le du c

2 3 4

finished the e mathematics mathematic athemati quiz in a shorter time

than

2.

.

Jordan and Ethan from han an hiked hik h rom the camping site to a waterfall.

Jordan reached waterfall in 4 hours 7 minutes. Ethan ed the he wate wa e waterfall aterfall in 2 219 minutes. Who was hiking for the reached the longer time? me?

Hours ourss

Minutes M Minut

1

2

3 4

hiked for a longer time than 14

.

Hands On

3.

ati on

2.

Take turns in rolling the dice. Move your counter forward orward ard the number of spaces shown on the dice. ay the he incorrect incorre Say the time in minutes and seconds. If you say time, go back to the start.

The first player to the finish is the winner.

60 s

Re g

144 s

20 0s

s 7 10

134 s

374 s

195 s

188 s

420 s s 315

9s 0 1

ed u

1.

29 5s 30 1s

s 9 8

34 7s 20 9

s

15

At Home Convert the times to seconds.

Re ga le du ca to n

1.

de to o school. school (a) It takes Chelsea 4 minutes 35 seconds to ride ool in seconds? secon How long does it take Chelsea to ride to school min =

4 min 35 s

s

s

4 min 35 s =

=

s+

s

s

seconds to ride to school.

It takes Chelsea

(b) In a game of basketball, ketball, ball, Wyatt scored the first goal in conds. ds. How long lon lo did it take for Wyatt to 3 minutes 14 seconds. score the first goal al in seconds? secon second min =

3 min 14 s

s

s

3 min 14 s = =

s+

s

Wyatt score sc scored the first goal in

16

s

seconds.

2.

Convert the times to minutes and seconds. (a) Blake chatted with his friends for 173 seconds. How long did Blake chat for in minutes and seconds?

173 s =

s

Re ga le du ca ti

s+ min

=

s

or Blake chatted with his friends for

min

s.

(b) Jordan finished a science quiz in 311 seconds. How long did he conds? take in minutes and seconds?

311 s =

s+

=

s

min

s

shed hed the tth science en quiz in Jordan finished

min

s.

(c) Sophie seconds e took k 287 sec second to row lake. w across cross the lake How take in ow long ong did she sh ta seconds? minutes nutes and seco sec 287 s =

=

Sophie took Sophi So

s+

s

min

s

min

s to row across the lake.

17

3.

Convert the times to minutes.

Re ga le du ca tio

(a) Students have 1 hour 35 minutes to finish a science exam. How many minutes do they have to finish the exam?? h=

1 h 35 min

min

min

1 h 35 min =

=

min +

min n

min

Students have

minutes utes to finish finis fini the science exam.

(b) Wyatt went fishing for 4 hours 26 minutes.

How long did Wyatt att go fishing for f in minutes? h=

4 h 26 min

min

min

4 h 26 min =

=

min + min

fishing for Wyatt went fish

18

in min

minutes. tes.

Convert the times to hours and minutes. co to o (a) It takes 155 minutes to travel from San Francisco Sacramento by train. How long is the train ride de in n hours and minutes?

Re ga le du ca tio n

4.

155 min =

min +

=

min

h

min

h

The train ride is

min. min

nver takes 192 minutes. (b) A flight from Miami to Denver ke in hours hour and minutes?

How long does the flightt take 192 min =

min n+

min i

h

=

akes kes The flight takes

min

h

min. in

(c) Wyatt did his homework for 205 minutes. How long did he homew do hiss homework omework for in hours and minutes? utes?

205 05 min =

=

min + h

Wyatt W yatt tt did his homework for

min

min

h

min.

19

Expressing 12-hour and 24-hour Tim Time

tio n

Let’s Learn

Re ga le d

The times on the departure board are shown in 24-hour 4-hour our time. p.m p When we use 24-hour time, we do not need to use a.m. or p.m.

When using 24-hour is expressed as 00 00. hourr time, midnight mid m 12:00 a.m.

6:00 0 a.m. a.m

00 00

06 00

In 24-hour hour time you normally don’t mally don say o’clock.

20

12:0 12:00 noon 12 00

6:00 p.m.

18 00

12:00 a.m.

00 00

For 18 00, we say eighteen hundred hours.

Re ga le du ca tio n

To convert times between noon and midnight into 24-hour time, you add 12 to the hours. To convert times between noon n and nd midnight from 24-hour time to 12-hour time, you subtract ractt 12 from the hours and add p.m.

Chelsea arrives home from school at 4:15 p.m.

Express the time Chelsea arrives home in 24-hour hour our time.

4 + 12 = 16

12-h 12-hour time: 4:15 p.m.

4:1 four fifteen p.m. fo 24-hour time: 16 15 sixteen fifteen

Chelsea goes to bed at 21 35.

Express the time Chelsea helsea else goes es to bed in 12-hour time.

21 – 12 = 9

24-hour time: 21 35 twenty-one thirty-five 12-hour time: 9:35 p.m. nine thirty-five p.m.

21

Let’s Practice Write the times in 24-hour time.

Re ga le du ca tio n

1.

(a)

(b)

1:15 1:115

3:30 0

Morning:

Morning: rning

Afternoon:

Afternoon: Afternoon

(c)

(d) d)

11:50 11:50

9:25 9:25

Morning:

Morning:

Night:

Night:

(e)

(f)

9:05 9:0 05

7:45 7:45

22

Morning: Morning

Morning:

Night: h

Night:

Write the times in 12-hour time using a.m. and p.m. (a)

(b)

(c)

(d)

(e)

(f)

Re ga le du ca tio n

2.

3.

Complete the table.

Flight Departures partu JFK International Airport

City

Departure (12-hour)

Los Angeles ngeles

1:45 a.m.

07 35

Miami Dallas Dal

Washington Wa

Departure (24-hour time)

3:40 p.m.

20 20

23

At Home

ga le du ca tio n

Complete the table.

School Camp Activities Program

Activity

12-hour Time

Breakfast

7:45 a.m.

Hike to Waterfall Swimming

24-hour hour Time

10 110

m.

11:50 a.m.

Lunch

12 30

Hike to Caves

1:35 35 p.m.

Cave Exploration

2:25 25 p.m.

Dinner

18 45

Campfire So ngs Songs

20 05

24

Duration of Time

ion

Let’s Learn

Re ga le du ca

Blake and Ethan went to the beach at 12 20. They left eft at 14 45.

How long were Blake and Ethan at the beach?

2h

12 20

25 min

14 20

14 45

2 h + 25 min = 2 h 25 min Ethan and Blake were at the he beach ach for 2 h 25 min.

Chelsea and Halle arrived d at the mall ma m at 13 30. They shopped until 15 15, then they wentt home.

How long ho h lo were Chelsea and Halle at the mall?

30 0 min

13 30

1h

14 00

15 min

15 00

15 15

1 h + 30 0 min m + 15 1 min = 1 h 45 min Chelsea and nd Halle were at the mall for 1 h 45 min.

25

ed uc a

n

Riley and her family left for the beach at 12 20. They arrived at the beach 4 hours 25 minutes later. What time did they arrive rive at the beach?

4h

12 20

25 2 min

16 20 16 45

4 hours after 12 20 is 16 20.

25 min after 16 20 is 16 45.

Riley and her family arrived at the at 16 45. he beach a

Re g

On Saturday, Ethan played ed tennis for 2 hours 50 minutes. He finished playing at 16 30.

0. What hat time did d Ethan start playing tennis?

20 min

13 40

30 min

14 00

14 3 30

2 hours before 16 30 is 14 30.

30 minutes before minu befo 14 30 is 14 00. nutes before nute be 20 minutes 14 00 is 13 40.

Ethan started te playing tennis at 13 40.

26

2h 16 30

Let’s Practice

Re ga le du ca tio n

Complete the word problems.

Use a timeline to show your working.

1.

ner was ready re Mrs. Jackson started cooking dinner at 17 20. Dinner ooking dinner? dinne dinner at 18 45. How long did Mrs. Jackson spend cooking

2.

A flight left Dallas airport att 05 50. It arriv arri arrived in Kansas City at 07 15. How long was the flight Dallas to Kansas City? ht from Da

3.

Halle visited sited d her grandmo grand grandmother at 11 25. She left her grandmother’s at 14 50. How long did Halle spend dmother’s her’s house hous a ing her grandmot grandmo visiting grandmother?

27

Riley and her sister arrived at the zoo at 10 25. They stayed at the zoo for 3 hours 35 minutes. What time did they ey leave leav eav the zoo?

Re ga le du ca tio n

4.

5.

Jordan arrived at school at 08 25.

5. Hiss English c class started 2 hours 40 minutes after he arrived. did rived. d. What time tim ti Jordan’s English class start?

6.

Wyatt washed ed the car with wi his h father for 1 hour 45 minutes.

They started car at 11 30. What time did they ed washing the th c finish washing ashing ng the car? car

28

On Saturday, Ethan played in the park for 2 hours 35 minutes. He left the park at 17 10. What time did Ethan an arrive at the park?

Re ga le du ca tio n

7.

8.

A tennis match lasted 5 hours 5 minutes. utes. The Th match finished at 21 25. What time did start? d the e tennis match m

9.

On Sunday, Sophie phie did housework ho hous for 3 hours 45 minutes.

She finished at 15 15. What time did Sophie ed the he housework housew start doing ng housework? housework

29

Solve It!

Re ga le du ca tio n

Use the map on the next page to answer the questions. ns.

Show your working.

1.

Riley hiked from the mountains, past the campsite, mpsite, to the pond. She arrived at the pond at 14 40. What Riley hat at time did Ril leave the mountains?

2.

Wyatt left the mountains ins ns at 10 25. He hiked past the waterfall to the forest. What did arrive at the forest? hat time tim t d Wyatt W

30

Mountains 25 min

35 min 15 min

45 min

ed

40 min n

50 m min

35 min

R

55 min

31

At Home

Re ga le du ca tio n

Complete the word problems.

Use a timeline to show your working.

1.

inished hed playing Mr. Woods started playing golf at 06 30. He finished golf at 11 15. How long did Mr. Woods spend playing golf?

2.

Mrs. Robinson opened herr pet store at 10 1 35. She stayed open for 5 hours 50 minutes. What at time did Mrs. Robinson close her pet store?

3.

A school hool play goes for f 3 hours 45 minutes. The play finishes at 20 35. What time did the school play start?

32

Blake’s family arrived at the lake at 12 50. They stayed at the lake for 4 hours 25 minutes. What time did Blake’s family amily ly leave le the lake?

Re ga le du ca tio n

4.

5.

Mr. Arlo opened his pizza shop at 15 45. He closed clos clo the shop at za shop op 23 30. How long was Mr. Arlo’s pizza open?

6.

Mr. Whyte raced ced d his car for fo 3 hours 55 minutes. He finished the race at 16 45.

5. What time did the car race start?

33

Word Problems

Re ga le du ca tio n

Let’s Learn

Halle did her mathematics homework for 2 hours 15 5 minutes.

She then did her science homework for 1 hour 35 minutes. nutes.

How long did Halle spend doing her mathematics science ics cs and scienc homework altogether?

2 h 15 min

1 h 35 min n science

mathematics

?

2 h 15 min + 1 h 35 min = 3 h + 15 min + 35 min = 3 h 50 min m

Halle spent 3 hours 50 minutes utes doing her he mathematics and science homework altogether. ether.

Blake spent 1 hour 25 minutes Blake’s father spent 3 nutes tes gardening. garde gard hours 30 minutes gardening.

How much longer did Blake’s father ard arde spend gardening??

1 h 25

?

Blake

ke’s ffather Blake’s 3 h 30

3 h 30 min – 1 h 25 min = 2 h + 30 min – 25 min = 2 h 5 min

Blake’s father spent 2 hours 5 minutes longer gardening than Blake. fat

34

Lola rides her horse every day for 45 minutes.

How long does Lola spend riding her horse in 5 days?

n

45 min

?

2

4 5

x

5

Re ga le du c

2 2 5 225 min = 3 h 45 min

In 5 days, Lola rides her horse for 3 hours 45 minutes.

Mr. Whyte buys a package of 8 golf lesso lessons for a total of 4 hours. less How long is one golf lesson? on?

First, convert nvert h hourss into the minutes. min

?

240 min

240 40 min ÷ 8 = 30 3 min m

Each lesson is 30 minutes long. h golf lesso

35

Let’s Practice

Re ga le du ca tio n

Complete the word problems. Show your working.

1.

ed for 3 hours hour Sophie ran for 1 hour 45 minutes. She then cycled cising g in all?

23 minutes. How long did Sophie spend exercising

2.

It took Jordan 3 hours 20 minutes nutes to reach the top of a mountain. Blake reached the he mountain top tto 1 hour 50 minutes faster than Jordan. How long ong g did it take Blake to reach the mountain top?

3.

Riley spent pentt 1 hour 48 minutes min m doing her homework. Halle spent urs 15 minutes doing doin d 3 hours her homework. How much longer did le spend pend doing he Halle her homework?

36

Riley takes 4 minutes 40 seconds to walk once around the school oval. How long will it take Riley to walk around d the he school oval 6 times?

Re ga le du ca tio n

4.

5.

On a hike, Halle and Sophie stopped ped for a break brea 6 times. Each break was the same number of minutes. The Th total break time ong was each break? was 1 hour 30 minutes. How long

6.

It takes Mrs. Whyte hyte 26 minutes minut mi to bake a cake. How long will it take Mrs. Whyte cakes? te to bake 8 c

37

At Home

Re ga le du ca tio n

Complete the word problems. Show your working.

1.

glish test.

Wyatt took 2 hours 15 minutes to revise for his English cience ce test. How Ho He took 3 hours 55 minutes to revise for his science ience ence test than tha his much longer did he take to revise for his science English test?

2.

Riley swims one lap of a swimming wimming pool poo in 3 minutes 35 seconds. How long doess it take to swim 9 laps of the ake for Riley Rile R swimming pool?

3.

Chelsea ea watched a series seri of 10 short stories. Each short story goess for the length of time. The whole series went for 3 he same len le hours How long was each short story? urs 20 minutes. H

38

Solve It!

Re ga le du ca tio n

Complete the word problems. Show your working.

1.

Halle took 35 minutes to walk from her house to the library.

5 She read in the library for 1 hour 45 minutes and left at 16 50.

What time did Halle leave her house?

2.

A chef takes 12 minutes ess to cook coo a pizza and 6 minutes to prepare a salad. needss to d.. He n t cook 8 pizzas and prepare 6 salads by 19 9 45. What is the latest time that the chef should startt cooking? oking?

39

Looking Back A news brief went for 4 minutes 43 seconds.

How long was the news brief in seconds?

Re ga le du ca tio n

1.

min =

4 min 43 s

s

s

4 min 43 s =

s+

s

s

=

The news brief lasted for

2.

seconds.

Blake cycled 2 kilometers in seconds. n 269 seconds second How long did it take in minutes utes and seconds? se s ?

269 s =

=

s+

s

min m

s

Blake cycled d 2 kilometers in

3.

40

min

Convert the times.

(a) 168 68 min n

=

h

min

b) 109 9 min (b)

=

h

min

((c) 3 h 22 min =

min

d) 4 h 4 (d) 411 m min =

min

s.

4.

Complete the table.

Re ga le du ca tio n

Departures – Eastern Bus Terminal

City

Hawthorne

Departure (12-hour)

6:45 a.m.

0 25 09

Inglewood

Santa Monica Malibu

Departure parture (24-hour 24-hour time) tim

6:40 p.m. .m.

21 55

5.

A chef takes 16 minutess to prepare a meal. How long will it take the chef to prepare pare e 9 such meals? me

6.

It took k Wyatt att 3 hours hour 12 minutes to jog around the lake 8 times.

How Wyatt to jog once around the lake? w long ong does it Wya Wy

41

Anchor Task

42

n

6

Measurement, Perimeter and Area

Benchmarks and Relative Sizes

Re ga le du ca tio n

Let’s Learn

These objects and distances can be used as benchmarks chmarks marks for customary units of measurement.

Benchmarks for Customary Units of Length

4 laps

about 1 inch (in)

about 1 foot (ft)

about out o 1 yard (y (yd)

about 1 mile (mi)

Benchmarks for Customary tomary Units Un of Volume

1 cup (c) (8 fluid ounces)

1 pint (pt) (pt

1 quart (qt)

1 half gallon

1 gallon (gal)

Benchmarks chmarks for Customary Units of Weight

about 1 ounce (oz)

about 1 pound (lb)

about 1 ton (T)

43

Let’s Practice Write the customary benchmark unit of measurement. ement. nt.

Re ga le du ca tio n

1.

(a) length of a paper clip

about 1

(c) weight of a loaf of bread

about 1

(e) width of a tablet bl computer omputer mputer

about bout 1

(g) g) length ngth of a baseball bas bat

about 1 44

ea in a cup (b) volume off tea

about out 1

(d) volume volume me of o juice in carton

about 1

(f) weight of a small car

about 1

(h) weight of a cookie

about 1

2.

Circle an appropriate customary unit of measurement. ycle e (b) weight of a bicycle

pounds

ed uc ati

on

(a) weight of an apple

tons

ounces

(c) height of a palm tree

inches

miles

feet eet

Re ga

(e) length of a tennis is court ourt

inches hes

yards

miles m

(g) weight eight of a tiger tige cub

ounces pounds

tons

ounces ces

pounds pounds

tons

(d) length ngth of a marker m

iinches in

feet

yards

(f (f) volume of water in a tub

gallons

cups

pints

(h) distance from home to school

inches

feet

miles

45

3.

Circle the appropriate measurement. hoolba (b) weight of a full schoolba schoolbag

Re ga le du ca tio n

(a) punch in a punch bowl

4 cups

4 quarts

(c) length of a snake

2 inches

2 feet

(e) volume of milk in n a bowl

1 gallon lon

1p pint

(g) weight eight of a cell phone

6 ounces

46

6 pounds

4 ounces

4 pounds

(d) weight eight of a tr truck

5 pounds

5 tons

(f (f) distance ran in 1 hour

6 miles

6 yards

(h) length of a violin

14 feet

14 inches

At Home Find an object or distance to represent these benchmark chmark mark unit units of measurement around your home or school.

Re ga le du ca tio n

1.

(a)

Benchmarks for Customary Units ts of Length about 1 inch about 1 foot

about 1 yard about 1 mile

(b)

Benchmarks for Customary Units of Volume about 1 cup about 1 pint nt

ut 1 quart q about

out 1 gallon about

(c)

Benchmarks for Customary Units of Weight Benchma about 1 o ounce

about 1 pound ab about 1 ton

47

2.

Write 'more than', 'less than' or 'about'. (b) volume of milk in small carton

Re ga le du ca tio n

(a) weight of a kitten

1 ounce

(c) weight of a bowling ball

1 pound d

n a cup (e) volume of milk in

1 pin pint

ume of soda in a can (g) volume

1 gallon 48

1 half gallon

(d) weight basketball ht of a b

1 pound

(f height of an armchair (f)

1 foot

(h) weight of a skateboard

1 pound

3.

Write an appropriate customary unit of measurement. plerr (b) weight of a stapler

Re ga le du ca tio n

(a) width of a TV cabinet

about 6

(c) length g of bed

about 3

about out 4

(d) distance nce ran in 30 min

about a 3

(e) volume of waterr in bucket (f (f) weight of a small truck

out 2 about

(g) heigh height eightt of a door

about 6

about 6

(h) volume of milk in a milkshake

about 3 49

Let’s Learn

Re ga le du ca tio n

These objects and distances can be used as benchmarks arkss for metric units of measurement.

Benchmarks for Metric Units of Length th

width of nail

10-minute walk

about 1 millimeter about 1 centimeter

about bout 1 meter mete

Benchmarks for Metric Units ts of Volum Volume

5 drops d

about 1 milliliterr

about 1 liter

sa m

pl

e

Benchmarks rks for Me Metric Units of Weight

about 1 gram

50

about 1 kilogram

about 1 kilometer

Let’s Practice Write the metric benchmark unit of measurement.t.

Re ga le du ca tio n

1.

(a) water in a drink bottle

about 1

(c) weight of a pineapple

about 1

(e) width of a television e n

about bout 1

(g) g) height heigh eightt of a mountain mo

about 1

(b) weight off a feather

about out 1

(d) thickne thicknes thickness of a coin

about 1

(f) width of a marker

about 1

(h) liquid in an eye dropper

about 1 51

2.

Circle an appropriate metric unit of measurement.

grams

kilograms

(c) volume of water in a tub

liters

milliliters ters

Re ga

(e) length of a jogging ing track

centimeters ntimeters eters

ycle e (b) weight of a bicycle

ed uc ati on

(a) weight of a strawberry

kilometers kilom

kilograms ilograms rams

grams g

(d) length gth g of an a ant

centimeters c

millimeters

(f (f) length of a pencil

centimeters

meters

(g) weight eight of a hippopotamus hipp (h) weight of a gold ring

grams

52

kilograms

kilograms

grams

3.

Circle the appropriate metric measurement. ee in n a cup cu (b) volume of coffee

Re ga le du ca tio n

(a) weight of a grasshopper

5 grams

5 kilograms

(c) height of a slide

2 centimeters

2 meterss

(e) bottle of nail polish lish

50 milliliters iliters

50 liters lit

(g) weight eight of a pot plant

3 grams

3 kilograms

250 milliliters iters

250 liters 2 25

(d) volume me of water wa in a bottle

20 milliliters 2

20 liters

(f (f) weight of a calculator

50 kilograms

50 grams

(h) length of a ukulele

35 centimeters

35 meters

53

At Home Find an object or distance to represent these benchmark chmark mark un units of measurement around your home or school.

Re ga le du ca tio n

1.

(a)

Benchmarks for Metric Units of Length Len

about 1 millimeter

about 10 millimeters

about 10 centimeters about 1 meter

about 10 meters

(b)

Benchmarkss for Metr Metric Units of Volume

iter about 1 milliliter

about 10 m milliliters bout 1 liter about

(c)

Benchmarks for Metric Units of Weight Benchm

about 1 gram

about 10 grams

about 1 kilogram

54

2.

Write 'more than', 'less than' or 'about'. assroom room door (b) height of the classroom

Re ga le du ca tio n

(a) weight of a chair

1 kilogram

(c) liquid in a soap dispenser

1 liter ter

1 meter

(d) volume kitchen sink me of a k

1 liter

(f height of an armchair (f)

(e) carton of milk

1 lite liter

eight of a soda can (g) weight

10 grams

1 meter

(h) weight of a hamster

1 kilogram 55

3.

Write an appropriate metric unit of measurement. by (b) weight of a baby

Re ga le du ca tio n

(a) height of a giraffe

about 3

(c) medicine in a teaspoon

about 5

(e) weight of a motorbike torbike bike

out 200 about

(g) paint aint in a large p paint tin

about 6 56

about out 10 0

(d) distance nce walk wa walked in 15 min

about a 2

(f) (f length of a truck

about 8

(h) length of a football field

about 100

Solve It! Jordan has 10 dimes. He stacks them in a pile. Which hich metric units should Jordan use to measure the weight and height of the pile of coins?

2.

Halle wants to measure her own weight ght and height. h Which metric units should she use? e?

3.

A truck driver needs to o fill in the form below. Complete the form using appropriate customary units of measurement. propriat ropri usto

Re ga le du ca tio n

1.

57

Converting Customary Units

Re ga le du ca tio n

Let’s Learn

Use this table to help convert different units of length!

Customary Units ts of Length Leng 1 foot

12 inches (in (in)

inches (in) 36 inch

1 yard

feet (ft) 3 fee

5,280 feet (ft) 5

1 mile

1,760 yards (yd)

In 1 foot, there are 12 inches. So to convert feet fee to inches, we multiply the number of feet by y 12. bbon that is 3 feet in length.

Chelsea cuts a piece of ribbon How long is the ribbon in n inches? ches?

3 x 12 = 36

The ribbon is 36 inches hes in length. length len

To convert inches the number of inches by 12. ches es to feet, we w divide d Ethan needs that is 60 inches long. eds an electrical electrica cable c What length ength gth of electrical electrica cable does Ethan need in feet?

60 ÷ 12 = 5

electrical cable that is 5 feet in length.

Ethan ne needs an e

58

Customary Units of Volume 4 quarts (qt)

Re ga le du ca tio n

Use this table to help convert different units of volume!

1 gallon

8 pints (pt) 16 cups ups (c) 4 cups (c)

1 quart

2 pints (pt) 2 cups (c)

1 pint

16 fluid ounces (fl oz)

1 cup p

8 fluid flu ounces (fl oz)

In 1 gallon, there are 4 quarts. So o to convert gallons g to quarts, we multiply the number of gallons ons by 4. ith 3 gallons of fruit punch.

Ethan has a container with How many quarts of fruit uit punch unch are ar in the container?

3 x 4 = 12

There are 12 quarts punch in the container. artss of fruit punc pu

To convert quarts arts to gallons, gallo we divide the number of quarts by 4.

Halle buys milk from a mini-mart. How many gallons uys 16 quarts of m of milk k does oes she buy?

16 ÷ 4 = 4

Halle gallons of milk from the mini-mart. le buys buy 4 gal

59

Re ga le du ca tio n

Use this table to help convert different units of weight!

Customary Units off Weight Weig

1 pound (lb) 1 ton (T)

16 ounces unces (oz) (oz

2,000 pounds poun (lb)

In 1 pound, there are 16 ounces. So to convert onver pounds p to ounces, we multiply the number er of pounds by b 16.

A baker needs 3 pounds off butter ter to bake bak some cakes.

How many ounces of butter tter does he need? n 3 x 16 = 48

The baker needs 48 ounces unce of butter.

To convert ounces nces to pounds, pound we w divide the number of ounces by 16.

6.

Sophie's pett cat weighs 6 64 ounces. What is the weight of the cat in pounds? nds?

64 ÷ 16 = 4

The of Sophie's pet cat is 4 pounds. e weight wei So

60

Let’s Practice Convert the customary units to complete the tables. es.

Re ga le du ca tio n

1.

(a)

(b)

(c)

Feet

1

Inches

12

Yards

1

Feet

3

9

Miles

1

3

Pints

3

48

2

4

1

2

Quarts rts

Quarts Cups

4

3

5

8

1

3

4

5

4

Pints

(f)

5

8,800

Cups

(e)

5

0 3,520

Yards

(d)

2

1

2

3

5

16

61

Gallons

1

Pints

8

Gallons

1

3

5 32

Re ga le du ca tio n

(g)

(h)

(j)

(k)

Feet

1

Inches

12

Pounds

1

2

20

3

5

48

2

Ounces

32

Tons

2

nds 2,000 Pounds

62

4

8

Quarts

(i)

3

3

5

64

3

5

8,000

2.

Convert the units. Show your working. in

(b) 4 ft =

in n

Re ga le du ca tio n

(a) 2 ft =

(c) 4 gal =

qt

(d) 5 yd =

ft

fl oz

(e) 3 lb =

oz

(f) 2 c =

(g) 5 T =

lb

(h) 2 mi =

yd

c

(j)

6 qt =

pt

in

(l)

2 gal =

c

(i)

3 pt =

(k) 2 yd yd =

63

3.

Convert the units. Show your working. ft

(b) 18 ft =

yd

Re ga le du ca tio n

(a) 72 in =

(c) 3,520 yd =

(d) 8,000 000 lb =

T

(e) 32 c =

qt

(f) 3 gal =

c

(g) 60 ft =

yd d

(h) 64 oz =

lb

(i)

ft

(j)

24 qt =

gal

yd

(l)

2 pt =

fl oz

48 in n=

(k) 72 in =

64

mi

4.

Write >, < or = to fill in the blanks. Show your working.

4 lb

(b) 12 ft

4 yd

Re ga le du ca tio n

(a) 48 oz

(c) 4,000 yd

2 mi

(d) 5,000 000 lb

6T

(e) 62 in

2 yd

(f) 22 c

14 pt

(g) 5 gal

20 ptt

(h) 6 qt

16 c

(i)

4 lb

(k) 3 c

66 oz

(j)

15 pt

9 qt

2 24 fl oz

(l)

2 mi

4,000 yd

65

Hands On wn on Take turns in rolling a dice. Move forward the number shown wn in brackets. brackets. the dice. Convert the measurement to the unit shown Some rules: • If you answer incorrectly, go back to the start.t. s.

• If you land on a lotus, leap forward 3 spaces. ce es.

• If you land on a dragonfly, fly back 3 spaces.

START

6 yd d (ft) ft)

ed

2 lb (oz)

ga

1T (lb (lb)

5 qt (pt)

66

12 ft (yd)

8 yd (ft)

16 pt (gal)

1c (fl oz)

7T (lb)

10 pt (c)

eg

56 fl oz (c)

2 gal al (pt)

FINISH 67

Solve It! Mrs. Jones needs 4 pounds of apples to bake some me apple pple o pies. She has 52 ounces of apples. How many more ounces of le pies? Complete Comp apples does Mrs. Jones need to bake the apple the table to help you find the answer.

Pounds

Ounces

1

16

tio n

1.

2 3 4

Re ga le d

5 Mrs. Jones needs

2.

more oun ounces of apples.

Mr. Williams sells his milk per pint. He has 5 gallons of lk for $1 p milk. If Mr. Williams sells all of his milk, how much money will ams ms se he make? Complete mplete ete the th table to help you find the answer.

Gallons

Pints nts

1

8

2

3 4 5

If he sells ll all his milk, Mr. Williams will make $ 68

.

A hardware store sells garden hoses for $6 per yard. The distance from Jordan's tap to his garden is 14 feet. How much will Jordan pay for a hose that can reach his is garden? arden?

Complete the table to help you find the answer.

Yards

Feet

1 2

tio n

3.

3 4

Re ga le du

5 6

Jordan will pay $

4.

for a hose tto reach his garden.

baske There are 9 players on a basketb basketball team. During a game, each up of sports drink. d player drinks 6 cups Coach Davis has 4 gallons of sports drink.. How many cups m cu of sports drink will be left after mplete the ttable to help you find the answer. the game? Complete Gallons

Cups

1

2

3 4

re will be There

cups of sports drink left after the game.

69

At Home Convert the units. Show your working.

Re ga le du ca tio n

1.

70

(a) 4 lb =

oz

(b) 30 ft =

yd

(c) 3 yd =

in

(d) 7 T =

(e) 64 c =

gal

(f) (f 10 gal g =

qt

(g) 24 pt =

c

(h) 40 yd =

ft

(i)

150 ft =

yd

(j)

3 mi =

(k) 80 oz oz =

lb

(l)

32 fl oz =

lb l

yd

pt

2.

Write >, < or = to fill in the blanks. Show your working.

2 qt

(b) 21 ft

8 yd

Re ga le du ca tio n

(a) 9 c

(c) 2,700 yd

2 mi

(d) 5,000 000 lb

5T

3 pt

(e) 3 yd

108 in

(f) 40 fl oz o

(g) 4 gal

32 c

(h) 6 qt

(i)

6 lb

(k) 4 mi

100 oz

10,000 ft

(j)

48 fl oz

(l)

100 in

20 c

3 pt

3 yd

71

Converting Metric Units

le du ca tio n

Let’s Learn

Use this table to help convert different units of length!

Metric Units of Length ength

1 centimeter

10 millimeters (mm) (m

100 00 millimeters millimete (mm)

1 decimeter (dm)

10 centimeters (cm) centime

centimeters (cm) 100 cen

1 meter

1,000 1,0 millimeters (mm)

1 kilometer (km)

1,000 1 0 meters (m)

In 1 meter, there are 100 centimeters. timeters. eters. So to convert meters to centimeters, we multiply the by 100. he number mber of meters m

Re

The length of Chelsea's school hool bus is 7 meters.

How long is the school buss in centimeters? centim

7 x 100 = 700

The length of the school bus is 700 centimeters.

72

Re ga le du ca tio n

To convert centimeters to meters, we divide the number of centimeters by 100.

The height of a giraffe is 300 cm.

What is the height of the giraffe in meters?

300 ÷ 100 = 3

The height of the giraffe is 3 meters.

The chart below shows how convert between metric ow w to con units of length. ÷ 100

÷ 10

millimeterss (mm)

x 10

÷ 10

centimeter centimeters m) (cm)

÷ 10

decimeters (dm)

x 10

÷ 1,000

meters (m)

x 10

kilometers (km)

x 1,000

x 100

73

Metric Units of Volume 1,000 milliliters (ml)

al ed uc ati on

1 liter ( l )

rs to o milliliters, milliliters we In 1 liter, there are 1,000 milliliters. So to convert liters multiply the number of liters by 1,000. k. How many milliliters m A drink cooler contains 5 liters of sports drink. of sports drink are in the drink cooler?

5 x 1,000 = 5,000

dri in the cooler.

There are 5,000 milliliterss off sports drink To convert milliliters to liters,, we divide the number of div milliliters by 1,000.

R

Riley fills the kitchen chen n sink with 8,000 8,0 milliliters of water.

How many lite ers off water e in liters t are i the kitchen sink?

8,000 =8 00 ÷ 1,000 1 There are 8 liters of water in the kitchen sink.

74

Metric Units of Weight 1,000 grams (g)

Re ga le du ca tio n

1 kilogram (kg)

In 1 kilogram, there are 1,000 grams. So to convertt kilograms ograms to grams, we multiply the number of kilograms by 1,000.

A bag of oranges has a mass of 8 kilograms. s.

Find the mass of oranges in grams.

8 x 1,000 = 8,000

There are 8,000 grams off oranges. anges.

To convert grams to kilograms, grams, ams, we divide the number of grams by 1,000.

A tin of beans has as a mass of 4,000 4,0 grams. Find the mass of the tin of beans in kilograms. grams.

4,000 000 ÷ 1,000 = 4

The tin off beans has a mass of 4 kilograms. be

75

Let’s Practice Convert the metric units to complete the tables.

Re ga le du ca tio n

1.

(a)

(b)

Centimeters

1

Millimeters

10

Decimeters

1

2

Meters

2

Meters

4

1

3

Kilometers ometers Meters

76

4

20

1

2

50

3

5

400

ers Centimeters

(e)

5

30

Decimeters

(d)

5

40

Centimeters

(c)

3

1

4

2,000 3,000

5

(f)

1

Liters

2

3

5 4,000

Re ga le du ca tio n

Milliliters

(g)

2

Kilograms

1,000

Grams

2.

3

5

3,000

Convert the units. Show your working. rking. g.

(a) 2 m =

cm

(b) 4 dm =

cm

(c) 5 kg =

g

(d) ( 2 km =

dm

(e) 900 mll =

(g) 9 m =

l

cm

(f) 5,210 cm =

dm

(h) 7,000 ml =

l

77

11 kg =

g

(j)

52 km =

m

Re ga le du ca tio n

(i)

3.

(k) 190 cm =

dm

(l)

(m) 8,000 g =

kg

(n) 320 dm =

cm m

m

Write >, < or = to fill in the blanks. Show Sho Sh your working. (a) 12 m

78

233 m =

1,200 0 cm m

(b) 4,500 ml

(c) 6,000 00 g

5 kg

(d) 120 cm

(e) ( 32 dm

320 cm

(f) 290 dm

4l

10 m

3,800 mm

At Home Convert the units. Show your working.

Re ga le du ca tio n

1.

kg

(a) 6,000 g =

(c) 5 kg =

(e) 900 ml =

2.

g

l

(b) 4 dm =

cm

(d) 2 km m=

dm

(f)) 5,210 5,2 cm =

dm

Write >, < or = to fill in n the he blanks. blank S Show your working. (a) 5 km

(c) 1,200 00 g

(e) ( 5,990 mm m

1,200 ,2 cm ,20

(b) 980 ml

9l

12 k kg

(d) 96 dm

9,600 cm

4,000 cm

(f) 12 km

12,000 m

79

Hands On Take turns in rolling a dice. Move forward the number shown hown on the dice. Convert the metric measurement to the unit shown in brackets.

Some rules: • If you answer incorrectly, go back to the start.t.

• If you land on a honey pot, leap forward 3 spaces. aces.

• If you land on a bee, fly back 3 spaces.

START

ed

inner! er!

The first player to the beehive is the winner!

g

7k kg (g)

5l (ml) 10 km (m)

80

4,000 m (km)

ca t

22,000 g (kg)

36 cm (mm (mm)

11 km (m)

182 dm (cm)

ga l

10 cm (dm)

6,000 00 0 ml (l)

14 kg (g)

FINISH 81

Solve It! The distance from the camp ground to the waterfall fall iss 5 kilometers. Ethan has hiked for 3,200 meters. How many man more meters does Ethan need to hike to reach h the e waterfall? waterfall waterfa we wer.

Complete the table to help you find the answer.

Show your working.

Re ga le du ca tio n

1.

Kilometers

Meters

1

2

3 4 5

Ethan needs to hike another her

2.

meters.

Mrs. Jenkins needs 625 of ribbon to make a dress.

25 centimeters centime centim She buys a ribbon in length. After making the on that ttha is 7 meters me m dress, how much uch ribbon ribbo will Mrs. Jenkins have left? Complete the table to help p you find the answer. Show your working.

Meters

Centimeters Centimete

3 4 5 6 7

Mrs. Jenkins will have 82

centimeters of ribbon left.

Mrs. Watkins made 9 liters of fruit punch for a party of 15 people. Each person drank 500 milliliters of fruit punch. nch.

How much fruit punch was left after the party? Complete omplete plete the orking. g table to help you find the answer. Show your working.

Liters

Milliliters

5

on

3.

Re ga le du ca

6 7

8 9

10

There was

4.

milliliters iters of fruit punch pu p left.

e 20 cakes. cakes cak For each cake, he needs A baker needs to make e has 3 kilograms kil ki 250 grams of flour. He of flour. How many flo f oes the baker need? more kilogramss of flour does Kilograms

Grams

1

2

3 4 5 6

The baker needs another

kilograms of flour.

83

Perimeter

Re ga le du ca tio n

Let’s Learn

The total distance around an object or figure is called alled d its perimeter. We can find the perimeter of figuress and objects in different ways.

The figure below is an irregular shape. We e can an find the perimeter p by adding the lengths of each side.

8 in A

5 in

4 in

4 in

Perimeter A = 4 + 8 + 5 + 4 = 21

The perimeter of Figure gu A is 21 in. gure Find the perimeter ter of Figure B. 6 cm

m 4 cm

2 cm

B

6 cm

8 cm

Perimeter B = 4 + 6 + 2 + 6 + 8 = 26

The perimeter of Figure B is 26 cm.

84

Remember to include the correct unit of measurement when writing the perimeter.

Re ga le du ca tio n

We can use mathematical formulae to find the perimeter of rectangles and squares.

A square has four sides of equal length.

C

12 yd

Length Perimeter C = 4 x Length = 4 x 12 = 48

d.

The perimeter of Figure C is 48 yd.

How can you find ngths of a the side lengths square if you the u know th perimeter? rimeter?

he square squar is 52 5 in. Find the length of each side.

The perimeterr of the

Perimeter ter = 52 in

?

Side length = Perimeter ÷ 4 = 52 ÷ 4 = 13

The square e has h side lengths of 13 in.

85

Re ga le du ca tio n

p Riley wants to measure the perimeter of her swimming pool.

The swimming pool is in the shape of a rectangle.

What formula can she use to find the perimeter?

A rectangle ctangle has h posite sides of opposite equal leng length.

5m

10 m

Perimeter = (2 x Length) + (2 x Breadth) eadth) th) = (2 x 10) + (2 x 5) = 20 + 10 = 30

The perimeter of Riley's swimming wimming ming pool poo is 30 meters.

How can you find the breadth of a rectangle ectan if you know perimeter? the per

Find the breadth eadth dth of the rectangle. recta re

?

Perimeter = 20 ft

7 ft

The breadth of the rectangle is 3 ft.

86

Breadth + Breadth = Perimeter – 7 – 7 = 20 – 7 – 7 = 6 ft Breadth = 6 ÷ 2 = 3 ft

Re ga le du ca tio n

We can also find the perimeter of objects and figures by adding or subtracting to find unknown sides.

A farmer needs to put a fence around his paddock.

How much fencing does he need?

First find the lengths of side BC and side EF. 90 m

A

B

?

60 m

BC = AF – DE = 60 – 25 = 35 m

D

45 m

25

F

?

E

C

Now that we know all the side lengths, we can add to find the perimeter!

EF = AB – CD = 90 – 45 = 45 m

Perimeter erimete = AB erimeter A + BC B + CD + DE + EF + FA = 90 9 + 35 + 25 + 45 + 45 + 60 = 300 30 m The farmer needs 300 m of fencing.

87

Let’s Practice Find the perimeter of each figure.

Re ga le du ca tio n

1.

(a)

5 in

3 in

A

6 in

Perimeter A =

+

=

+

in

(b)

14 m

4m

4m

B

6m

18 m

Perimeter B =

+

=

(c)

+

+

+

m

8 yd

8 yd

C

6 yd

6 yd

5 yd

Perimeter C = Perimet P

= 88

11 yd

+

yd

+

+

+

+

2.

Find the perimeter of the squares.

Re ga le du ca tio n

(a) 22 ft

Perimeter of square =

x

=

ft

are = Perimeter of square

x

(b)

16 yd

=

yd

(c)

35 mm

Perimeter of square = Perimete Perim

=

x

mm

89

3.

Find the perimeter of the rectangles.

Re ga le du ca tio n

(a) 4 ft

7 ft

Perimeter of rectangle = (2 x =

+

=

ft

) + (2 2x

)

) + (2 x

)

(b)

9m

24 4m

Perimeter of rectangle ctangle ngle = (2 x =

+

=

m

(c)

20 in

120 in

Perimete of rectangle = ( Perimeter

90

x

=

+

=

in

)+(

x

)

Find the side lengths of the squares. (a)

Re ga le du ca tio n

4.

Perimeter = 88 m

Side length of square =

÷4

=

m

(b)

Perimeter = 36 in

Side length of square quare re =

=

÷

in

(c)

Perimeter = 144 cm

Side leng length of square =

=

÷

cm

91

5.

Find the length or breadth of the rectangles.

Re ga le du ca tio n

(a) 5 in

Perimeter = 30 in

Length + Length = 30 –

Length =

=

–

=

–

=

in

÷2 in

(b)

Perimeter = 50 yd Perim

?

18 8 yd y

Breadth eadth th + Breadt Breadth =

–

=

–

=

yd

Breadth = =

92

÷

yd

–

6.

Find the lengths of the unknown sides. Find the perimeter.

71 yd

A

B

Re ga le du ca tio n

(a)

C + DE AF = BC

23 yd

?

D 13 yd

=

+

=

m

C

17 yd

F

E

58 yd

Perimeter =

+

+

+

+

+

=

(b)

?

R

S

?

74 4m

P

Q

55 m

32 m

U

T

120 m

QR R = ST – PU

RS = TU – PQ

=

–

=

–

=

m

=

m

P Perimet Perimeter =

+

+

+

+

+

= 93

At Home Find the perimeter of each figure. Show your working. king..

Re ga le du ca tio n

1.

(a)

54 yd

22 yd

45 yd

32 yd

Perimeter =

(b)

54 m

68 m

32 m

30 m

771 m

Perimeter Pe Perime =

94

38 m

2.

Find the perimeter of the squares. Show your working. g

Re ga le du ca tio n

(a) 15 ft

Perimeter eterr =

(b)

Perimeter =

55 yd

(c)

42 mm

Perimeter =

95

3.

Find the perimeter of the rectangles. Show your working.

Re ga le du ca tio n

(a) 6 in

21 in

Perimeter =

(b)

60 m

Perimeter =

30 m

(c)

15 cm

95 cm 9

Perimeter erim =

96

4.

Find the length or breadth of the rectangles.

Re ga le du ca tio n

(a) Perimeter = 250 yd

15 yd

Length =

(b)

Perimeter er = 240 in

78 in

Breadth Bread =

97

5.

Find the perimeter of the figures. Show your working. (a)

15 m

B

Re ga le du ca tio n

A

19 m

30 m

D

C

?

?

F

E

42 m

Perimeter =

(b)

?

0 yd 10

10 yd

26 yd

18 yd

14 yd

?

53 yd

Perimeter i = 98

Solve It!

ca tio n

Halle's desk at home can be represented by the figure e below. low. ues and The figure is composed of 2 rectangles. Read the clues complete the table.

Clues: • AB has a length of 140 cm.

• AF and DC are of equal length.

• EF has a length of 100 cm.

• The perimeter of the desk is 480 cm.

A

Re ga l

F

B

E

C

D

Side

Length

AB BC CD DE EF FA 99

Area

Re ga le du ca tio n

Let’s Learn

The amount of space occupied by a shape or surface rface ce is called its area. Area is measured in square units. A square re unit is a square squ sq that has a side length of 1 unit.

We can use customary and metric units of length ength as a measurement for area.

The grid below is made up of squares of 1 cm. es with side lengths len We can measure the area of the shapes pes in square squa centimeters.

1 cm

1 cm

A

C

B

Shape pe

Length Le (cm)

Breadth (cm)

Area

A

7

1

7 cm2

B

6

3

18 cm2

C

5

5

25 cm2

What at pattern pat do d you notice about the length, breadth and area of the shapes?

What formula can we use to calculate the area of sha shapes rectangles and squares?

100

Re ga le du ca tio n

We can calculate the area of a square using the formula: Area of square = Side length x Side length mula: We can calculate the area of a rectangle using the formula: Area of rectangle = Length x Breadth

Let's use the formulae above to measure the area of the squares sq and rectangles below.

S

T

12 ft

50 yd

50 yd

9 ft

Area S = 50 x 50 0 = 250 yd2

Area T = 12 x 9 = 108 ft2

V

U

32 m

A Ar Area ea U = 32 x 8 = 256 2 m2

15 mi

8m

15 mi

Area V = 15 x 15 = 225 mi2

101

Re ga le du ca tio n

We can find the unknown side of a rectangle if we know one side length and the area. a of 3,000 m2.

The football field has a length of 100 m and an area Find the breadth of the football field.

100 m

Area = 3,000 m2

?

Breadth = Area ÷ 100 0 = 30 m

We can find the lengths of a square if we know e unknown nknown side sid le the area.

A square tile has an area of 81 cm. Find its side lengths. are o

Area A re = 8 811 cm cm2

?

Area of square = Side length x Side length 81 = 9 x 9 The tile has a side length of 9 cm.

102

Re ga le du ca tio n

A composite figure is a shape that is made of two or more shapes joined together. s.

The composite figure below is made of 2 rectangles.

How can you calculate the area?

12 m

5m

12 m

13 m

8m

To find the area of the composite posite te figure, we w can find the area of each rectangle and add them hem together.

12 m

5m

12 m

13 m

A

B

Area A = 13 x 12 = 156 m2

8m

Area B = 12 x 8 = 96 m2

Area of Figure = Area of Figure A + Area of Figure B = 156 + 96 = 252 m2

103

We can also divide the figure another way.

Re ga le du ca tio n

12 m 5m

C

12 m

13 m

8m

D

Area C = 12 x 5 = 60 m2

Area ea D = 24 4x8 = 192 2 m2

Area of Figure = Area of Figure C + Area of Figure Fig D = 60 + 192 = 252 m2

We can also make the composite omposite posite figur figure into a rectangle and subtract the unshaded figure ure from the th shaded figure.

12 1 m

5m

12 m

13 m

8m

Area unshaded = 12 x 5 Area ea shaded = 24 2 x 13 2 = 60 m2 = 312 m Area a of F Figure = Area shaded – Area unshaded = 312 – 60 = 252 m2

104

Let’s Practice Find the area of each figure. Complete the table.

Re ga le du ca tio n

1.

1 in

1 in

A

B

C

E

D

Shape

Length

Breadth

Area

A B

C

D E

105

(a) (b) (c) (d)

Draw a square with an area of 4 cm2. Label it 'A'.

Draw a square with an area of 9 cm2. Label it 'B'..

Draw a rectangle with an area of 14 cm2. Label el it 'C'.

C'. bel it 'D'.

Draw a rectangle with an area of 21 cm2. Label

Re ga le du ca tio n

2.

1 cm

1 cm

106

3.

Find the area of each figure.

Re ga le du ca tio n

(a)

M

90 yd

Area square M =

x

yd2

=

(b)

6 ft

N

21 ft

Area N = =

x

ft2

(c)

O

40 m

110 m

Area O = =

x

m2

107

(d)

Re ga le du ca tio n

25 in

P

Area square P =

x

in2

=

(e)

4 ft

Q

26 ft

Area Q = =

x

ft2

(f)

R

26 m

A Area R= =

108

x

m2

12 m

Find the length or breadth of the rectangles and squares. (a)

Re ga le du ca tio n

4.

Area = 30 in2

5 in

Length = 30 ÷ =

?

in

9m

(b)

Area = 63 m2

?

Breadth readth =

÷

=

m

(c)

Area o of square = Side length x Side length

2

Area = 144 yd

144 =

Side length = Sid

x

yd

?

(d)

Area of square = Side length x Side length

Area = 400 mm2 A ?

=

Side length =

x

mm

109

5.

Find the area of the composite figures. Show your working. (a)

Re ga le du ca tio n

10 m

3m

6m

6m

3m

4m

Area =

(b)

14 ft

4 ft

7 ft

4 ft

7 ft

Area = 110

2 ft

4m

8m

Re ga le du ca tio n

(c)

7m

6m

7m

10 m

5m

6m

4m

23 m

Area =

33 ft

(d)

7 ft

13 ft

10 0 ft

5 ft

3 ft

17 ft

Area = 111

Hands On

on

Work in pairs to find 4 rectangle-shaped objects inside your classroom lassroom room and an in the schoolyard. Find the area and perimeter of each object ect and nd record your findings in the table on the next page.

112

113

Appropriate unit of length

Picture

Perimeter

Area

Re ga le du ca tio n

Object

At Home Find the area of the squares. Show your working.

Re ga le du ca tio n

1.

(a)

12 in

A

Area ea =

(b)

B

21 ft

Area =

(c)

C

35 mm

Area =

114

2.

Find the area of the rectangles. Show your working.

Re ga le du ca tio n

(a) 15 yd

Q

70 yd

Area =

(b)

32 cm m

R

16 c cm

(c)

Area =

12 cm m

S

22 cm

Area = 115

3.

Find the length or breadth of the rectangles and squares.

Re ga le du ca tio n

(a) Area = 35 in2

?

5 in

=

15 m

(b)

?

Area = 120 m2

=

(c)

Area = 64 y yd2 ?

=

116

Find the perimeter and area of the composite figures.

Show your working.

Re ga le du ca tio n

4.

(a)

16 in

6 in

7 in

3 in

Perimeter =

14 in n

7 in

7 iin

Area = 117

23 yd

Re ga le du ca tio n

(b) 5 yd

5 yd

4y yd

14 yd

7 yd

5 yd

Perimeter = 118

Area =

64 m

(c)

Re ga le du ca tio n

15 m 12 m

44 m 44

29 m

20 m

8m 38

90 m

Perimeter i =

Area = 119

Word Problems

Re ga le du ca tio n

Use the chart below to help you answer the word problems. blems. ms.

Length

Metric

Customary stomary

1 centimeter = 10 millimeters 1 decimeter = 10 centimeters 1 meter = 100 centimeters

1 foot = 12 inches hes 1 yard = 3 feet et 1 mile = 1,760 60 yards

1 kilometer = 1,000 meters

Mass

Metric

C Customary

p 1 pound = 16 ounces 1 ton = 2,000 pounds

1 kilogram = 1,000 grams

Volume

Metric

Customary

1 liter = 1,000 milliliters

1 cup = 8 fluid ounces 1 pint = 2 cups 1 quart = 2 pints 1 gallon = 8 pints

Time

1 minute = 60 seconds 1 hour = 60 minutes 1 day = 24 hours 1 week = 7 days 1 year = 52 weeks

120

Let’s Practice ograms. ams.

Blake chooses a bowling ball with a weight of 9 kilograms.

How many grams does the bowling ball weigh?

Re ga le du ca tio n

1.

grams gra gr

2.

ck Express xpress dep d The cost to send a parcel at Truck depends on the weight of the parcel. How much to send a ch will it cost Sophie S parcel that weighs 40 ounces? es?

Price List

Up to 1 lb – $25 1 lb too 2 lb b – $30 2 lb too 3 lb b – $34 3lb to 4 lb – $38 Please s co c ntact us for packages oveer 4 lb.

3.

$

Ethan practices cticess tennis for f 45 4 minutes every evening. How many hours does Ethan practice for in 1 week? ourss and minutes minu

h

min

121

A chef made 5 gallons of soup. A serving of soup is 1 cup.

How many servings did the chef make?

Re ga le du ca tio n

4.

cups

5.

Mr. Patel wants to build a fence around ound d his square squar squa vegetable patch. The vegetable patch has an area of 36 m2. atel need?

What length of fencing does Mr. Patel

m

6.

A flight from Tallahassee takes 2 hours 45 minutes. m Dallas allas to Tal Tallah How long is the minutes? e flight in min

min

122

Ethan arrived at the snowfields at 11:15 a.m.

He skied for 1 hour and 40 minutes before having lunch. nch. h.

What time did Ethan have lunch?

Re ga le du ca tio n

7.

8.

Blake is building a wooden his favourite den frame around aro ar photograph. The length photograph is 8 inches. th off the photo phot The breadth of the photograph otograph is 6 inches.

How much wood does es Blake need? ne

in

123

Mr. Roberts has a rectangular garden that is 12 m by 7 m.

He installs a square hot tub within the garden area thatt has ha a side length of 3 m. Find the remaining area of his garden rden

Re ga le du ca tio n

9.

m2

10. A shoebox lid has a perimeter of 120 cm and a length of perimet perim 38 cm. Whatt is the breadt breadth of the shoebox lid? bre

Breadth = 124

Mrs. Windfield's kitchen is 5 yards long and 3 yards wide. Tiles cost $4 per square foot. How much will it cost Mrs. Windfie Windfield dfie to buy enough tiles to cover her kitchen floor?

Re ga le du ca tio n

11.

$

12. Mr. Martinez needs 7,800 mll of coo cooking oil for his restaurant. ,800 0m The oil is sold in 2 l bottles les which whic are $6 each. How much money does Mr. Martinez M ez need to buy the oil?

$

125

At Home Sophie finished a running race in 240 seconds. ce?

How many minutes did she take to finish the race?

Re ga le du ca tio n

1.

min

2.

Mr. Jackson needs 13 quarts of paintt to paint pain his living room. ns and nd cost $2 The paint comes in 1-gallon tins $22 each. How many on need? How much will he spend? tins of paint does Mr. Jackson

tins

3.

$

An alligator or hass a length of 4 meters. What is the length of the alligator in decimeters? ecimeters

dm

126

Ethan threw a 32-ounce discus a distance of 63 feet. What was the weight of the discus in pounds? What was the distance he threw the discus in yards?

Re ga le du ca tio n

4.

5.

lb The base of a square gazebo hass a side length of 14 feet.

What is the area of the base of the gazebo?

yd

ft2

6.

A rectangular ar birthday card ca has a perimeter of 30 inches.

The height of the he card is i 10 inches. Find the breadth.

in

127

7.

Chelsea's family is building a new house. What is the area of the house? What is the area of the lawn?

5m

uc ati on

10 m

6m

2m

3m

3m

4m

8m

4m

Re ga

7m

128

10 m

Solve It!

Re ga le du ca tio n

Mr. Rossi is building a fence to make a rectangular paddock ddock ck on h and d width wid his farm. He bought 96 yards of fencing. What length ck with the should he build the fence in order to get a paddock working largest area? Draw a diagram and show your working.

length =

width = 129

Looking Back Circle the appropriate measurement.

Re ga le du ca tio n

1.

(a) weight of a pencil case

1 ounce

1 pound

(c) length of a bench

5 inches hes

130

5 gallon gallons

5 pints

(d) v volume olume of perfume in a bottle

5 feet feet

(e) height ight of a mountai mou mountain

2 kilometers

aterr in a large bottle (b) volume of water

50 milliliters

50 liters

(f) weight of a doll house

2 meters

3 grams

3 kilograms

2.

Convert the units. Show your working. ft

(b) 30 ft =

yd d

Re ga le du ca tio n

(a) 60 in =

(c) 1,760 yd =

(e) 32 c =

(g) 20 cm =

(i)

4,000 00 g =

(k) 3,000 ml =

mi

pt

(d) 3,000 000 lb =

(f) 2 gal =

mm m

(h) 4 l =

T

c

ml

kg

(j)

7 km =

m

l

(l)

2 dm =

cm

131

Find the perimeter of the rectangle. Show your working.

Re ga le du ca tio n

3.

12 yd

42 yd

Perimeter =

4.

Find the area and perimeterr of the composite figure. compo comp Show your working.

8 cm

3 cm

6 cm

4 cm

1 cm

Perimeter = 132

Area =

Sophie makes a basket as a gift for her grandmother.

She also bakes 6 cupcakes and puts them into the basket basket. ket The total mass of the basket and cupcakes is 1 kg.. bask The mass of 1 cupcake is 140 g. Find the mass off the basket.

Re ga le du ca tio n

5.

Mass o of basket =

6.

g

es $5 per pe square meter to clean A cleaning company charges carpets. Jordan's living square in shape with a side ng room is squ length of 6 m. How much ch would woul it cost to clean the carpet in Jordan's living room? oom

$

133

Angles

Anchor Task

1 34

on

7

Identifying and Naming Angles

Re ga le du ca tio n

Let’s Learn

ndpoint. point.

An angle is formed by two rays with a common endpoint. alled a vertex erte The common endpoint where the rays meet is called vertex.

A

We use the symbol to n name angles.

x

C

B

Rays AC and BC meet at vertex an angle. tex C to form a We can name the angle ACB or o BCA BCA. We can also name the angle ngle e x. thin hin shap Angles are also formed within shapes. es and an 3 angles. ngle A triangle has 3 sides A rectangle has 4 sides es and 4 angles.

D

P

x

y

z

E

x= y= z =

EDF = DEF = EF = EFD

F FDE FED DFE

F

Q

a

b

c

d

S

R

a b c d

= = = =

SPQ = PQR = PSR = SRQ =

QPS RQP RSP QRS

1 35

Let’s Practice Circle the diagrams that show angles.

Re ga le du ca tio n

1.

2.

(a)

(b)

(c)

(d)

(e)

(f)

Circle the angless in each h shape. shape Fill in the blanks.

(a)

(b)

sides sid

angles

(c) c)

angles

sides

angles

(d)

sides 1 36

sides

angles

3.

Name the angles. (a)

(b)

F

Re ga le du ca tio n

T

S

U

(c)

G

E

(d)

B

X

A

Y

C

W

4.

Name the angles in other her ways. ways

(a)

C

(b)

D

a

V

b

h

k

d

l

c

F

E

a=

W

i

j

Y

X

Z

i =

=

CFE

c =

=

VZY

=

WXY

k=

=

CDE

1 37

At Home Name the angles.

Re ga le du ca tio n

1.

G

(a)

H

N

(b)

q

x

I

M

x=

q=

(c)

P

d) (d)

R

m

z

Q

P

O

z=

2.

m=

Name the angles.

(a) S

T

n

m

p

(b)

W

Y

e

U

p =

c

X

a

o

V

d

b

V

U

a=

=

VUT

m =

=

WXY

=

UYX

e =

= 1 38

Q

UTS

O

3.

Name the angles in other ways. (a)

N

e

Re ga le du ca tio n

M

f

d

g

i

O

h

P

d=

=

=

NPO

e =

ONM

i = g=

(b) Z

r

m

W

n

o

p

Y

q

X

p =

=

=

r =

XZW

XYZ

q = n =

1 39

Anchor Task

140

n

Comparing Angles

Let’s Learn

Re ga le du ca tio n

Compare the angles made by the popsicle sticks.

Which angle is bigger? Which angle is smaller?

a

b

Angle a is bigger than angle b.

Angle b is smaller than angle a.

y the popsicle sticks. s Compare the angles made by ich angle is the smallest?

Which angle is the biggest? Which

x

y

z

Angle than angle y and angle z. Angle x is the biggest. gle x is bigger tha Ang y is smaller Angle sma tthan angle x and angle z. Angle y is the smallest.

1 41

Re ga le du ca t

n

Take a piece of paper and fold it two times as shown.

The angle formed at the corner of the paperr is called a right angle. pendicular lines.

We show a right angle by drawing 2 perpendicular Use your folded piece of paper to o compare mpare the angles below.

s

Angle s is bigger than a right angle.

142

t

Angle t is a right angle.

u

Angle u is smaller than a right angle.

Let’s Practice Check the bigger angle.

Re ga le du ca tio n

1.

(a)

(b)

2.

Check the smaller angle. er a (a)

(b) b)

1 43

3.

Check the biggest angle. Cross the smallest angle.

Re ga le du ca tio n

(a)

(b)

1 44

Circle the right angles. Use a piece of paper to help you.

Re ga le du ca tio n

4.

1 45

Circle the right angle in each shape.

eg

ed uc ati on

5.

146

Check the angles smaller than a right angle.

7.

Check the angles bigger ggerr than a right rig angle.

Re ga

ed uc ati on

6.

1 47

At Home Check the biggest angle. Cross the smallest angle.

Re ga le du ca tio n

1.

(a)

(b)

148

Check the box that applies to each angle. Use a piece of paper to help you.

Re ga le du ca tio n

2.

Angle

Smaller than a right angle

Right angle

Bigger ger than a angle right ang

1 49

Measuring Angles

Re ga le du ca tio n

Let’s Learn

A protractor is used to measure and draw angless in degrees.

Let's look at the different parts of a protractor.

outer scale

inner scale

center enter p point

ba base line

Angle ABC below is a right ht angle. A right rig angle is 90 degrees. o We write 90 degrees ass 90 .

C

A

B

150

We use straight lines to show right angles.

ati on

Let's look at how to measure an angle using a protractor.

Step 2

Step 1

Align the e base line of the protractor tor with the ray DE.

Align the center point i of the protractor on vertex E. Step 3

DEF.

ed

Measure

F

D

E

Line EF aligns with the 50o mark on the protractor. DEF = 50o Angles that are lesss than 90 degrees egr are called acute angles.

XYZ..

R

Find

Z

X

Y

Line YZ aligns with the 125o mark on the protractor. XYZ = 125o ali Angles that are more than 90 degrees are called obtuse angles.

1 51

Let’s Practice Write the angle. Check if the angle is acute or obtuse. use.

Re ga le du ca tio n

1.

(a)

C

ABC = acut acute ob obtuse

A

B

(b)

O

MNO = acute obtuse

M

N

W

(c)

UVW = acute obtuse

U

V

152

(d)

Re ga le du ca tio n

G

EFG G= ac acute obtuse

E

F

(e)

J

H

HIJ = acute obtuse

I

(f)

K

L

KLM = acute obtuse

M

153

2.

Measure the angle. Check if the angle is acute or obtuse.

A

Re ga le du ca tio n

(a)

ABC BC = acute obtu obtuse

C

B

(b) D

F

E

DEF = acute obtuse

O

(c)

MNO = acute obtuse

M

(d)

N

X

XYZ = acute obtuse

Y

154

Z

3.

Estimate then measure the angles. (b)

Re ga le du ca tio n

(a)

t

s

(c)

(d)

v

u

(e)

(f)

x

w

(g)

(h)

z

y

Angle A

s

t

u

v

w

x

y

z

Estimate Measure

155

Hands On With a partner, use your popsicle angle-maker to make an angle.

2.

w an angle an Trace the inside of the angle-maker to draw on a sheet of paper. Label the rays, vertex and angle.

3.

Estimate and measure the angle.

4.

Make different angles and complete te the he table below. be

Re

ca tio n

1.

Angle

Estimate Esti Measure

156

At Home Measure the angle. Check if the angle is acute or obtuse. use.

Re ga le du ca tio n

1.

(a)

O

M

(b)

N

MNO NO = acute obtu obtus obtuse

D

DEF = acute obtuse

F

E

(c)

A

ABC = acute obtuse

C

B

(d)

X

XYZ = acute obtuse

Y

Z

157

2.

Estimate then measure the angles. (b)

Re ga le du ca tio n

(a)

a

b

(d)

(c)

c

d

(e)

(f)

f

e

Angle A

Estimate Measure

1 58

a

b

c

d

e

f

Solve It!

Re ga le du ca tio n

Measure the angles Halle turns as she walks to the waterfall. aterfall. fall.

A

B

ABC = A

C

BCD =

E

DEF =

D

CDE =

F

159

Drawing Angles

Re ga le du ca tio n

Let’s Learn

We can use a protractor and ruler to draw angles. s.

Let's draw an acute angle of 60o.

Step 1

Use a ruler l to draw d a straight line. Label the line AB.

A

B

Step 2

Align line AB to the base line of the protractor. Align point A to the center point.

A

B

C

Step 3

Draw a dot at the 60o mark on the inner scale e of the bel it point C protractor. Label C.

A

C

Step p4

Use se a ruler to draw d a line to point A to point C. connect poin Label the angle. bel th

60o

A

160

B

B

Re ga le du ca tio n

Let's draw an obtuse angle of 142o.

Step 1

Use a ruler to draw a straight line. Label the line YZ.

Z

Y

Step 2

Align line YZ to the base line of the protractor. Align point Z to the center point.

Y

Z

Step 3

X

o

Draw a dot at the 142 mark rk on the outer scale of the protractor. Label it poin point X.

Y

Z

Step 4

Use a ruler to o draw a line li to connect point Z to point poin X. Label the e angle.

X

142o

Y

Z

1 61

Let’s Practice Draw a line from the center point to make each angle. ngle. e. (a) 30o

Re ga l

(b) 72o

(c) 144o

1 62

uc ati on

1.

2.

Draw and label the angles.

ABC = 50o

Re ga le du ca tio n

(a)

B

(b)

A

DEF = 114o

D

(c)

E

GHI = 158o

H

G

1 63

3.

Draw and label the angles.

ABC = 50o

Re ga le du ca tio n

(a)

1 64

(b)

MNO = 129o

(c)

PQR = 95o

Hands On Draw and label an angle. Have your friend use a protractor to measure your angle.

Angle 1:

Friend's riend's meas measurement: =

o

Angle 2:

=

o

Friend's measurement: =

o

Angle 3:

=

o

Friend's measurement: =

o

=

o

1 65

At Home Draw a line from the center point to make each angle. ngle. e. (a) 76o

Re ga l

(b) 124o

(c) 156o

1 66

uc ati on

1.

Draw and label the angles. (a)

ABC = 34o

Re ga le du ca tio n

2.

B

(b)

A

DEF = 148o

D

(c)

E

GHI = 28o

H

G

1 67

3.

Draw and label the angles.

JKL = 121o

Re ga le du ca tio n

(a)

168

(b)

XYZ = 162o

(c)

DEF = 77o

Solve It!

Re ga le du ca tio n

Draw the times on the clocks. Measure the angle between ween n the hour hand and the minute hand. (a) 3:00

=

(b) 1:20

=

(c) 5:00

=

(d) 4:20

=

(e) 5:10

=

(f) 2:30

=

1 69

Properties of Angles

Re ga le du ca tio n

Let’s Learn

When an angle is comprised of non-overlapping parts, rts, the angle ang measure is the sum of the angles of the smallerr parts.

Let's find

ABC.

A

ABC = ABD + DBC = 30o + 75o = 105o

D

75o

30o

C

B

ABC = 105o

When an angle is comprised parts, we can omp d of non-overlapping no subtract the smaller err parts tto find d the unknown angle measure.

WOZ = 160o Let's find x.

Y

W

x = WOZ – WOY = 160o – 108o = 52o

108 1 o

x

O

x = 52o

170

Z

Line ST is a straight line.

Add SVU and UVT.

on

The sum of the angles on a straigh straight line iss 18 180o.

Re ga le du ca

U

S

T

V

1180o

SVU +

UVT = 126o + 54o = 180o

Line AB is a straight line.

Find y.

46 6

A

1126 2 o

B

O

61o

o

y

D

C

y = 180o – AO AOC – o = 180 80 – 46o – 6 61o = 73o

54o

180o

BOD

61o

46o

y

1 71

Lines OA, OB and OC meet at point O. Find the sum of the angles.

Re ga le du ca tio n

A

The sum of the angles at a pointt is 360o.

155o

65o

O

B

140o

C

o

360

155o

AOB +

140o

BOC +

65o

COA = 155o + 140o + 65o = 360o

Lines OP, OQ, OR and OS meet at point O. Find x.

S

P

76o

x

59o

O

Q

140 40o

R

360o

76o

59o 5

140o

x ?

o

x = 360 – S SOP – POQ – o = 360 0 – 776o – 59o – 140o = 85o

172

QOR

Let’s Practice Find the unknown angle. Show your working.

Re ga le du ca tio n

1.

a=

LON = 100o

(a)

L

M

a

22o

N

O

AOD = 129o

(b)

AOB =

B

C

A

50o 5

64o 6

D

O

POR =

P

(c)

Q

42o

12o

O

R

1 73

2.

Find the unknown angle. Show your working.

x=

Re ga le du ca tio n

(a) PS is a straight line.

R

Q

x

102o

64o

P

S

O

w=

(b) EH is a straight line.

F

G

60o

E

w

H

O

r=

(c) LP is a straight ight line.

N

M

L

174

49o

r

13o

O

O

16o

P

3.

Find the unknown angle. Show your working.

m=

Re ga le du ca tio n

(a) All straight lines meet at point F. C

B

59o

44o

A

m

F

82o

15o

D

E

(b) All straight lines meet at point N. N JK is a straight line.

a=

J

I

0o 50

N

84o

a

34o 3

M

L

K

1 75

Solve It!

Re ga le du ca tio n

Read the clues and find the unknown angles. (a) AB is a straight line. a is half the size of c. b is 3 times the size of a.

b

c

a

A

B

a=

b=

c=

ht lines. nes. (b) PQ and RS are straight ROQ = 130º

P

n

m

O

R

n

S

m

Q

m=

176

n=

At Home

Re ga le du ca tio n

Find the unknown angle. Show your working.

AOB =

AOC = 139º

(a)

C

O

67o

B

A

(b)

y=

S

R

y

50 0o

Q

T

MQN =

(c) LP is a straight raight ght line.

M N

O

11o

87o

75o

L

Q

P

1 77

UYV =

(d) All straight lines meet at point Y.

Re ga le du ca tio n

U

148o Y

T

37o

83

o

V

74o

X

W

(e) All straight lines meet at point nt E. A

E

32o

B

C

D

178

AED =

Let’s Practice

Sophie tries to perform a 360º spin while ice skating. ting. e does She manages to spin 327º. How much more she need to turn to complete a full spin?

Re ga le d

1.

tio n

Word Problems

2.

y degrees does doe the minute hand of a How many k turn in 15 minute minu clock minutes?

1 79

Ethan and his friends are erecting a flag pole. How much u ght? more do they have to turn the pole to make it upright?

le du ca tio n

3.

38º

4.

A wrecking ball is pulled lled d back by b an angle of 28º and released. ang thatt is 5º less than the release angle.

It swings to an angle nd the total angle gle that th the wrecking ball swings.

Find

?

Re g

28º

180

At Home The Leaning Tower of Pisa forms an angle of 86º to the ground as shown below. How many degreess must ust it turn to become fully upright?

Re ga le du ca tio n

1.

86o

2.

A Ferris wheel eel turns 42º in 1 minute.

How much h does es it turn in 5 minutes?

1 81

Look at the time shown on the clock below to answer the questions.

Re ga le du ca tio n

3.

(a) How many degrees has ass the minute hand h turned since 1 o'clock? k?

(b) The minute another 60º. What is the time now? he minut min e hand han turns tu

182

Looking Back Name the angles.

Re ga le du ca tio n

1.

B

v

C

w

x

y

z

u

A

D

v=

=

=

BCD

z=

2.

BAD

y=

w=

Check the bigger er angle. an a

(a)

(b) b)

1 83

Check the box that applies to each angle. Use a piece of paper to help you.

Re ga le du ca tio n

3.

Angle

184

Smaller than a right angle

Right angle

ger than a Bigger right ang angle

Draw and label the angles. (a)

WXY = 115o

(b)

p = 64o

(c)

PQR = 90o

Re ga le du ca tio n

4.

1 85

t = 120o

Re ga le du ca tio n

(d)

ABC = 160o

(e)

5.

Find the unknown nkno own angle. angle Show Sh your working.

TOU =

SOU = 135º

(a)

T

U

S

186

O

ROQ =

(b) QT is a straight line and

SOT.

ROS =

S

Re ga le du ca tio n

R

50o

Q

T

O

HOI H =

(c) HK is a straight line.

I

J

15o

H

O

K

AOB =

(d) AE is a straight traight ight line.

A

B

O

52o 5

28o

C

20o

E

D

1 87

(e) All straight lines meet at a point.

k=

Re ga le du ca tio n

R

120o

S

k

83o

Q

T

(f) All straight lines meet att point E. A

B

7o

34o

E

95o 9

D

188

C

AED =

The roof of a school building is the shape of a triangle and has a flag on top. Find the angle formed between the flag ag pole and the roof.

Re ga le du ca tio n

6.

?

75o

7.

When the e minute inute hand on a clock is pointing at 10, how many degreess must it turn to point at 12? t p

1 89

Symmetry

Re ga le du ca tio n

8

Anchor Task

190

1 91

Re ga le du ca tio n

Identifying Symmetric Figures

Re ga le du ca tio n

Let’s Learn

Take a sheet of paper and fold it in half as shown.

When the paper is folded along ong g the dotted line, the halves formed are exactly the same shape. pe. The e dotted line is a line of symmetry.

Fold the paper again ass shown. own.

A figure can have more than one linee of symmetry.

This dotted line is also a a line of symmetry.

192

Re ga le du ca tio n

Now fold the paper as shown.

When folded along the dotted line, shapes formed are not e, the e two sha exactly the same shape. The dotted otted line is not no a line of symmetry.

A symmetric figure has att least st one line line of symmetry. sym The figures below are symmetric figures. mmetric etric figur gurres. gure

The figures any es below elow do not no have h y lines line of symmetry.

They are re not symmetric figures.

1 93

Let’s Practice (a) Check the lines of symmetry. ry.

Cross the lines that are not lines of symmetry.

Re ga le du ca tio n

1.

(b) Is a hexagon a symmetric mmetric ric figure? figure Explain your answer.

2.

(a) Check the lines ines nes of o symmetry. m Cross the lines that are not ymmetry. metry. lines of symmetry.

H w many Ho ma lines l (b) How of symmetry does the heart have?

1 94

3.

Use a ruler to draw a line of symmetry through each figure. (b)

Re ga le du ca tio n

(a)

(c)

(d)

(e)

(f)

(g)

(h)

1 95

4.

Shade the symmetric figures and draw a line of symmetry. (b)

Re ga le du ca tio n

(a)

196

(c)

(d)

(e)

(f) (

(g)

(h)

Hands On In small groups, walk around your schoolyard and search arch for symmetric figures.

2.

Draw four symmetric figures in the space below. elow. Draw a line lin of symmetry through each figure.

Re ga

ed uc

tio n

1.

1 97

At Home Check the lines of symmetry. Cross the lines that are not lines of symmetry.

Re ga le du ca tio n

1.

1 98

(a)

(b)

(c)

(d) (d

(e)

(f)

Put a cross through the figures that are not symmetric.

Shade and use a ruler to draw a line of symmetry through hrough ough the symmetric figures.

Re ga le du ca tio n

2.

(a)

(b)

(c)

(d) (d

(e)

(f)

1 99

Let’s Learn Trace this shape on a folded sheet of paper.

Re ga le d

Cut out the shape and unfold the paper.

ca tio n

Drawing Symmetric Figures

The figure made has two wo identical dentical halves. h It is a symmetrical figure. g gur We can also draw w symmetric ymmetric ffigures using square grid paper.

20 0

Hands On 1.

Fold a sheet of paper in half. alf.

Trace and cut out a symmetric figure.

2.

Trace or paste the figure in the space below. Draw a line of symmetry.

2 01

Let’s Practice

Re ga le du ca tio n

In each grid, the dotted line is a line of symmetry.

Draw lines to form the symmetric figure. (a)

(b)

(c)

(d)

(e)

20 2

Hands On Draw half of a symmetric figure on each square grid.

Draw the line of symmetry.

Re ga le du ca tio n

1.

2.

Swap books with a partner and have them complete each ea symmetric figure.

(a)

(b)

(c)

(d)

2 03

At Home In each grid, the dotted line is a line of symmetry.

Draw lines to form the symmetric figure.

Re ga le du ca tio n

1.

(a)

(b)

(c)

(d) d)

(e)

20 4

Solve It!

Re ga le du ca tio n

We can use square grid paper to make symmetric patterns. atterns. rns.

Complete these symmetric patterns. erns. (a)

(b)

(c)

(d)

2 05

Looking Back Check the lines of symmetry. Cross the lines that are not lines of symmetry.

Re ga le du ca tio n

1.

2.

(a)

(b)

(c)

(d)

Use a ruler to draw w a line lin of symmetry through each figure.

(a)

206

(b)

In each grid, the dotted line is a line of symmetry.

Draw lines to form the symmetric figure. (a)

(b)

(c)

(d)

Re ga le du ca tio n

3.

4.

Draw a symmetric mmetric etric figure figur on each square grid.

Draw the symmetry. e line e of symmetr symm (a)

(b)

2 07

Line Plots and Line Graphs

Anchor Task

208

on

9

uc ati on Length of Pencilss Tally

Tota Total

Re

Length

2 09

Interpreting and Creating Line Plots lot

uc ati on

Let’s Learn

A line plot shows how frequently data occurs along a number line.

An 'X' is placed above a number each time it occurs in the data set.

Length of Pencils Pencil Length Total th Tally ally To 3

3 in

1 in 4 1 3 in 2 3 3 in 4

5

4 in

2

3

Blake and Wyatt measured the length of all of the pencils in their pencil cases. They first recorded the data in a tally and then into a line plot.

3 in

Most of the pencils 1 were 3 2 in in.

210

2

1 3 in 4

1 3 2 in

3 3 4 in

4 in

Re ga

4

The shortest pencils were 3 in The longest were 4 in.

The City Zoo measured the heights of the giraffes in the African Animals enclosure. The data is shown in the line plot below.

Re ga le du ca

1 14 ft 2

15 ft

1 15 ft 2

16 ft

1 16 6 ft 2

1 The line plot shows that mostt off the giraffe giraffes are 15 ft tall.

2 1 It shows that the shortest st giraffe raffe is 14 ft tall and the tallest giraffes 2 1 are 16 ft tall.

2 What is the difference in height between the shortest and tallest giraffes?

1 1 16 – 14 = 2 2 2

The difference in h height between the shortest and the tallest raffes is 2 ft. giraffes

211

Let’s Practice The line plot shows the ages of children at Chelsea's a's birthday party.

Ages of Children

Re ga le du ca tio n

1.

6

7

8

9

10 1

(a) How many children are 9 years old?

(b) How many children dren are 6 years year yea old?

(c) How many ny children are a 8 years or older?

(d) How are 6 or 7 years old? ow many children childre child

(e) What is ( i the age difference between the youngest and children? oldest ch

212

Sophie surveyed the children in her class to find out how many people live in their households. She recorded the data in a line plot.

Re ga le du ca tio n

2.

Number of People in Household

3

4

5

6

7

(a) How many householdss have 6 people? peopl peop

seholds olds hav have 4 people? (b) How many households

(c) How many any households household have h more than 4 people?

(d) How w many households house hous have fewer than 6 people?

(e)) How How many m people did Sophie survey?

213

Jordan loves to collect rare coins. The line plot below shows the denominations of the coins in his collection. on.

Jordan's Rare Coins

Re ga le du ca tio n

3.

pennies

nickels

dimess

quarte quarters half dollars

(a) How many nickels does Jordan n have?

(b) How many dimess and d quarters does Jordan have?

(c) How many than dimes does Jordan have? y more quarters qu q

(d) How than half dollars does Jordan have? w many fewer fewe nickels nic

(e) How H w many Ho man of o Jordan's coins are not quarters?

21 4

The line plot below shows the number of each item sold at the school cafeteria at lunch time.

Cafeteria Sales

Re ga le du ca tio n

4.

pies

sandwiches hot dogss

salads salad

apples

(a) Which item sold the least? ast?

(b) Which item sold d the e most?

(c) How many any more apples app were sold than sandwiches?

(d) How w many items item were sold in all?

(e) fewer pies and sandwiches were sold than ( ) How How many m a apples? salads and

215

On a holiday to Mermaid Beach, Wyatt went fishing with his dad and brother every day. The table below shows ws the number of fish Wyatt caught each day.

du ca tio n

5.

Fish Caught at Mermaid Beach Day

Number of Fish Caught

Wed

4

Thurs Fri Sat Sun

3 6 6 4

eg

(a) Represent the data in the he table in a line plot.

21 6

Re ga le du ca tio n

(b) On which two days did Wyatt catch the most fish?

(c ) On which day did Wyatt catch the fewest fish? h?

(d) On which days did Wyatt catch an number of fish? n equal qual numbe numb

(e) How many fish were caught ht on n Wednesday Wednes Wednesd to Friday?

(f) How many fish were e caught aught on the th weekend?

(g) How many more mo fish h were caught on the weekend compared and Thursday? d to o Wednesday Wedn Wed

(h) On Saturday, Satur turday, day, Wyatt's Wyatt brother caught twice as many fish as Wy man fish did Wyatt's brother catch on Saturday?

Wyatt.. How many

( (i)

Frid On Friday, Wyatt and his dad caught 20 fish in all. ma fish did Wyatt's dad catch on Friday?

How many

217

Ethan measured the length of the nails in his dad's toolbox.

He made a tally to record the data.

Re ga le du ca tio n

6.

Length of Nails

Length (in)

Tally

21 2 23 4 3

31 4 31 2 33 4

(a) Represent the e data in the ttable in a line plot.

21 8

Re ga le du ca tio n

(b) What was the length of the longest nails?

(c ) What was the length of the shortest nails?

(d) What was the most common nail length? gth?

(e) What was the least common mon nail length? lengt

(f) How many nails were shorter than th t 3 inches?

(g) What wass the in length between the shortest e difference differ diffe gestt nails? and longest

tota length le (h) What is the total of all the 3-inch nails?

(i)

What is i the th total length of all the 2 1 -inch nails?

2

219

Hands On 1.

22 0

Use a ruler to measure the animals.

Record your data in a tally on the next page.

ed uc

Length eng of Animals

Length ((in)

Tally

221

Use the data in your tally to create a line plot.

Re ga le du ca tio n

2.

3.

(a) What is the most common mmon mon animal length? l

(b) What is the leastt common length? ommon animal a

longe a (c) What was the longest animal? What was its length?

(d) What animal? What was its length? hat was was the shortest sh

was (e) What W wa the difference in length between the shortest animals? and longest an lon

22 2

At Home Blake surveyed his classmates about the time they y spent pent d the data doing homework on the weekend. He presented he collected in the line plot below.

Re ga le du ca tio n

1.

Hours Doing Homework on Weekend end nd

1 2

3 4

1

11 4

11 2

13 4

(a) How many students for 45 minutes? entss did homework homew

(b) How many ny students tudents did d homework for less than 1 hour?

(c) How did homework for 90 minutes or more? ow many students student stud

(d) (d What was w the t most common amount of time spent hom doing homework?

223

Wyatt surveyed his friends about how many houses they visited on Halloween. He presented his data in a line plot. ot.

ed uc ati on

2.

Houses Visited on Halloween

0

5

10

15

20 2

20+

(a) How many students did nott visit any houses? h

(b) How many students entss visited 10 or o fewer houses?

a

(c) How many visited more than 20 houses? ny students tudents vi

Re

(d) How visited 20 houses than students ow many fewer fewe students s who o visited 10 houses? ho

was (e) What w as the most common number of houses visited by stude b students on Halloween?

224

Ethan measured the length of the fishing gear in his tackle box.

He represented the data in a line plot.

Length of Fishing Gear (in)

Re ga le du ca tio n

3.

1 2

1

11 4

11 2

13 4

2

ortest items in the tackle box? (a) What length are the shortest

e the e longest items iti (b) What length are in the tackle box?

difference ferenc in length between the longest and (c) What is the dif st items? ems? shortest

(d) What is the total tota length of the items that are 1 1 in long? tota 4

many items in the tackle box are shorter than 2 in? (e) How ma

225

Sophie surveyed the students in her class to see how far each student ran during the school fun run.

She recorded her data in a tally.

Re ga le du ca tio n

4.

School Fun Run

Distance (mi)

Students

2

2

1 2

3

3

1 2

4

4

1 2

(a) Represent the e data d in the ttable in a line plot.

22 6

Re ga le du ca tio n

(b) How many students ran 4 1 mi?

2

(c) How many students ran 2 1 miles?

2

(d) How many students ran 3 miles or less? ss?

(e) How many students ran 3 miles es or more? more

(f) What was the difference erence e between betwe betwee the shortest and longest distance ran? n?

(g) Which distances stances nces were wer ran by at least 5 students?

ow many students student stude (h) How ran more than 4 miles?

(i (i)

What was w the t total distance ran by all students who ran tha 4 miles? more than

227

Hands On e more more Gather 15-20 objects from around your home that are than 2 inches and less than 6 inches in length.

2.

bj t to t the e Use a ruler to measure the length of each object 1 nearest inch.

4

3.

Record your data in a tally, then representt the the data data in a line plot.

Re ga le d

1.

Tally

22 8

Write four questions that can an be be answered an by interpreting the data in your line plot. Ask the to your classmates e questions q sti rs and record their answers.

Re ga le

4.

uc ati on

Line Plot

Questions

229

Interpreting and Creating Line Graphs ra

Re ga le du ca tio n

Let’s Learn

1.

Mr. Whyte recorded the amount of fuel he used ed every month mon for five months. He recorded the data in the table below.

Fuel Consumption

Month

Fuel Used (l)

Jan

50

Feb

125

Mar

100

Apr

0 100

May

150

u To help us interpret th the data, wee can repre represent the data in a lline graph.

Mr. Whyte's hyte's e's Fuel Co Consumption

Fuel (l)

150

100

50 0

Jan Ja

Feb

Mar

Apr

May

Month

What things can you interpret about Mr. Whyte's fuel consumption?

2 30

Re ga le du ca tio n

(a) In which month did Mr. Whyte consume the most fuel?

Mr. Whyte consumed the most fuel in May. 0 l off fuel? fue (b) In which months did Mr. Whyte consume 100 Mr. Whyte consumed 100 l of fuel in March h and nd in April.

April

(c) How much did the fuel consumption increase ncrease crease from January to February?

From January to February, fuel consumption nsumption umption increased inc by 75 l.

The line graph below shows the number to a zoo for mber of visitors vis a period of one week.

Zoo Visitors rs – Monday to t Sunday

Visitors

2.

1,500 1,250 1,000 750 500 250 0

Mon on

Tues

Wed We

Thurs Day

Fri

Sat

Sun

(a) On which hich two two days da were there fewer than 700 visitors?

Tuesday had fewer than 700 visitors. ay and Wednesday We Wed

(b) b) How Ho ow many man more mo visitors were there on Friday than on Wednesday?

Wednesd Wedn There There were 500 more visitors on Friday than on Wednesday. (c) visitors were there on the weekend? c) How Ho many m There here were 2,750 visitors on the weekend.

2 31

Let’s Practice The line graph below shows bakery sales for one week. ek.

Bakery Sales – Monday to Sunday day

Re ga le du ca tio n

1.

Sales ($)

3,000 2,000 1,000 0

Mon

Tues

Wed

Thurss Day

Frii

Sat

Sun

(a) What were the bakery y sales on Saturday?

Satu Sat

al sales on o Monday and Tuesday? (b) What were the total

(c) What was the difference between the lowest sales and the differe highest est sales?

(d) d) On n how how many days were sales greater than $750?

(e) What was W w the difference in sales from Thursday to Friday?

23 2

The line graph below shows the number of visitors to Mermaid Beach in the morning.

Mermaid Beach Visitors

Re ga le du ca tio n

2.

Visitors

150

100 50 0

06 00 06 30 07 00 077 30 08 00 08 30 09 00 Time

(a) At what time was the number umber of visitors visito the highest? visi

(b) At what time was as the he number of visitors the lowest?

(c) How many ny visitors were we at Mermaid Beach at 07 00?

(d) What was in visitors from 07 00 to 07 30? was the increase incr in

(e) What was ( w the difference in visitors from 08 30 to 09 00?

2 33

Riley planted a seedling. She measured the height of the plant every day for five days. She recorded her measurements ments nts in the table below.

n

3.

ght Seedling Height Day

Height (cm)

Tues

1

Wed

2

1 2

3

Fri

4

Sat

5

Re ga le du

Thur

(a) the data from the ( ) Represent Repre table tab in a line graph below.

Seedling Height Seedlin

5

Height (cm)

4

3

2

1

0

Tues

Wed

Thurs Day

2 34

Fri

Sat

Re ga le du ca tio n

p (b) What was the height of the seedling when Riley planted it?

(c) How much did the plant grow from Tuesday ay to Wednesday?

(d) On which day was the seedling 3 cm m tall?

1 (e) When did the seedling grow row w by 1 cm in one day?

2

(f) When did the seedling edling ng grow the th least in one day?

(g) How many did the seedling grow in five days? ny centimeters centimete ntime

4.

The table able below shows sho the monthly shoe sales from a sporting rting g goods store. store Shoe Sales (Jan to Jun)

Mo Month

Jan

Feb

Mar

Apr

May

Jun

Sale Sales ($)

200

250

150

400

300

200

(a) Represent the data in a line graph on the next page.

2 35

Shoe Sales (Jan to Jun)

Sales ($)

Re ga le du ca tio n

500

100

0

Month

(b) What were the shoe e sales les for the th month of March?

(c) What was the he difference d ence in i shoe sales from April to May?

(d) In which hich month month w was sshoe sales the greatest?

(e) months e) In which mo m nth were shoe sales greater than $200?

(f) was f) What W w the total shoe sales for April, May and June?

23 6

Hands On

uc ati on

Riley recorded the distances she jogged every day forr one e week.

She recorded the data in a table.

Distances Ran Day Distance (km)

Tues

1 2

4

2

Wed

Thur

4

6

Fri

4

1 2

Sat 3

1 2

Sun 4

1 2

epresent esent the data d Use a computer graphic tool to represent in a line graph. Give your graph a title and axes. Print and nd label the a ow. paste the graph in the space below.

R

1.

Mon

2.

With a classmate, talk about the things the line graph shows. cl 2 37

At Home Blake and Wyatt counted the number of birds in the he local ocal wetlands every Saturday for six weeks.

Re ga le du ca tio n

1.

Wetland Bird Population

Number of Birds

40

30 20 10

0

1

2

3

4

5

6

W Week

(a) How many birds were ere at the wetlands w in week 2?

(b) How many ny more birds bir were in the wetlands in week 5 ek 4? than in week

weeks d (c) In which weeks did they spot the fewest birds?

wee 7, Blake and Wyatt spotted 15 fewer birds than in (d) In week w week 6. How many birds did they observe?

238

The line graph below shows the total number of enrolled students at Miami Primary School from 2015 to 2020.

0.

Miami Primary School Enrolments

Re ga le du ca tio n

2.

Students Enrolled

500 400

300 200

0

2015

2016

20177 2018 8 Year

2019 2

2020

(a) How many more students udents nts enrolled in 2016 compared to 2015?

(b) What happened from 2016 to 2019? pened ened to enrollments rol .

(c) What number of enrollments from 2018 at iss the total total n num to 2020?

0

(d Miami Primary Prim P (d) School predicts enrollments will increase stu by 150 students in 2021. If they are correct, how many s student students will enroll in 2021?

2 39

The table below shows the mass of meat sold each weekday at Peter's Fine Meats.

n

3.

Meat Sold Mass (kg)

Mon

225

Tue

250

Wed

175

Re ga le du c

Day

Thur

200

Fri

150

(a) the data from the a) Represent Represe res table in a line graph.

Meat eat Sold (Mon (M – Fri)

Mass (kg)

250

50 0

Day

24 0

Re ga le du ca tio n

(b) On which day was the most meat sold?

(c) How much meat was sold on Friday?

(d) How much more meat was sold on n Monday than tha Friday?

(e) How much meat was sold from to Friday? m Wednesday Wednes

(f) On Saturday, Peter'ss Fine twice as much meat e Meats sold s as Friday. How much uch meat was sold on Saturday?

(g) On Sunday, Meats had a sale. They sold three y, Peter's Fine F uch meat as they did on Saturday. How much times ass much Sund S meat was sold on Sunday?

(h) What hat was was the total to mass of meat sold from Friday to Sunday?

Sunday

2 41

Hands On In small groups, use a thermometer to record the outdoor door air temperature every hour from 9 a.m. until 1 p.m. Record ord your data in the table below.

uc ati on

1.

Air Temperature Time Temperature (oC)

In the space below, represent the he data ta in a lin liline graph.

R

2.

24 2

9 a.m. 10 a.m. 11 a.m. 12 p.m. 1 p.m.

Interpret the data in your line graph. (a) What was the temperature at 9 a.m.?

Re ga le du ca tio n

3.

(b) How did the temperature change in the he e first hour?

mperature erature between bet be (c) What was the difference in temperature 10 a.m. and 1 p.m.?

(d) At what time was the e temperature emperature the highest?

(e) At what time wass the he temperature temp tempe the lowest?

(f) Based on the he data in i your yo graph, what do you predict the temperature perature ature will be b at 5 p.m.? Explain your answer.

2 43

Looking Back The line plot shows the number of questions students ents got correct in a 10-question math quiz.

Correct Answers in Math Quiz

6

7

ed uc ati on

1.

8

9

10

ered d all questi (a) How many students answered questions correctly?

(b) How many students ts answered swered 7 questions correctly?

a

(c) How many students stude studen answered nsw less than 9 rrectly? questionss correctly?

Re

was the he difference diffe d (d) What was between the lowest and hest scores? highest

(e) How students took the quiz in all?

How many man m

244

The table below shows the amount of sports drink children drank after a football match.

ati on

2.

Sports Drink Consumption Amount (cups) Children

1 2

2

3

3

1

1 2

3

5

5

2

1 2

4

3

2

3

Re ga l

(a) Represent the data in a line plot.

(b) How many y children drank dra less than 3 cups of sports drink?

(c) How drank more than 2 cups of sports drink?

Ho ow many children child

(d) How much muc sports drink did the children drink in all?

2 45

3.

The line graph below shows the temperature of water in a beaker over 1 hour.

Temperature (oC)

Re ga le du ca tio n

Water Temperature

100 80

60 40 20 0

1:00 p.m.

1:10 p.m.

1:20 p.m.

1:30 p.m. p.m

1:40 p.m. p.m

1:50 p.m. 2:00 p.m.

Time

(a) What was the temperature ture of the water wa at 1:10 p.m.? w

(b) What was the increase from 1:10 p.m. ncrease ease in temperature tem to 1:20 p.m.?

(c) How did change from 1:40 p.m. d the e temperature temperatur tempera to 2:00 00 p.m.?

d) What was was the increase in temperature from 1:00 p.m. (d) p.m to 1:30 p.m.?

246

The table below shows the amount of money Chelsea saved each month for 6 months.

Re ga le du ca tio n

4.

Chelsea's Savings

Month

Feb

Mar

Apr

May

Jun un

Jul

Savings ($)

35

40

10

50

45 5

25

(a) Represent the data in a line graph.

(b) In which month nth di did Chelsea save $40 more than the previouss month? onth?

n which ch month month did Chelsea save $20 less than the (c) In evious month? previous

(d) How muc much did Chelsea save from April to July?

2 47

Act It Out

ati on

10 Problem Solving

Re ga le d

Example Two tennis teams are competing against each h other. There are ay y each member me mem 4 players on each team. Each player must play of ches es are playe the opposing team. How many tennis matches played in all?

There re are a total tota of 12 pairs of players. So, 12 matches must be played in n all.

248

6 people attend a meeting. If everyone shakes hands with one another, how many handshakes occur?

Re ga le du ca tio n

1.

2 49

2.

Re ga le du ca tio n

Use 9 toothpicks U to make this shape.

(a) Take away 3 toothpicks to make 1 triangle. angle. Cross out the toothpicks you removed. Draw the he shapes hapes formed. for

(b) Take away ay 3 toothpick toothpic toothpicks to make 2 triangles.

Draw the he shapes hapes formed. formed form

2 50

3.

Re ga le du ca tio n

Use 12 toothpicks to make this shape.

(a) Take away 2 toothpicks to make 2 squares. quares.

Cross out the toothpicks you removed. emoved. oved Draw the shapes formed.

(b) Take away way 4 toothpicks toothpic to make 2 squares.

Cross out the you removed. he toothpicks toothp Draw w the e shapes formed. form f

2 51

In small groups, sit in a circle. Take turns counting upward from 1. If the number is a multiple of 3, say 'fizz!' instead ead d of the number. If the number is a multiple of 5, say 'buzz!' z!' instead stead of d 5, say sa the number. If the number is a multiple of both 3 and 'fizz buzz!' instead of the number.

Re ga le du ca tio n

4.

(a) At what number will 'fizz buzz!' be said for the 3rd time? tim

(b) At 50, how many ma times mes has ha 'fizz!', 'buzz!' and 'fizz buzz!' been called d out?

25 2

Draw a Model

Re ga le du

tio n

Example st of a racer is A bicycle shop orders a scooter and a racer. The cost 4. Find nd the total tota 3 times the cost of a scooter. A scooter costs $354. cost of the shop’s order.

First, let’s find the cost of a racer.r. $354

scooter

1

x

racer

3 15 4 3

1 0 6 2

?

A racer costs ts $1,062.

1,062. $354 54

$ $1,062

scooter

racer

1 10 6 2 +

3 5 4 1 4 1 6

?

1,062 062 + 354 3 = 1,416 So, the cost of the shop’s order is $1,416. e total tot co

253

502 strawberries were picked at a strawberry farm. 46 of the strawberries were rotten and were put in the compost. ost.. The Th rest were packed into punnets of 8 strawberries. How w many punnets were there in all?

Re ga le du ca tio n

1.

254

Sophie buys 9 meters of ribbon to wrap presents and has $30 left over. If she bought 6 meters of ribbon, she would d have ave $51 left. How much money did Sophie have originally??

Re ga le du ca tio n

2.

255

163 pupils each donate $12 for a charity fundraiser. The money is collected and shared equally between 3 charities.

How much money does each charity receive?

Re ga le du ca tio n

3.

25 6

Halle loves to read. She reads 24 pages of a book per day for 3 weeks. In the 4th week, she had a lot of homework work k and a read 10 pages less per day. Find the total number of pages she read in the 4 weeks.

Re ga le du ca tio n

4.

257

Guess-and-Check

Re ga le du ca tio n

Example An automotive factory produces motorcycles and cars. Itt produces 3 times as many cars than motorcycles.. In one day it es. How man many used a total of 168 wheels to produce the vehicles. motorcycles and cars were made?

rcycles. cles. Find the th total Start with a guess on the number of motorcycles. wheels and then increase or decrease depending epending nding on tthe outcome.

Let's start with 3 motorcycles.

Motorcycles Motorcycle wheels

Cars

Car ar whee wheels

Total wheels

3

6

9

36

42

10

20

0 30

120

140

11

22

3 33

132

154

12

24

36

144

168

Our first guess wass far too to low. So we increased to 10 and got a result closer to 168.

1 motorcycle at a time until 8. We then increased in we found the correct orrect ect answer. answer The automotive 12 motorcycles and 36 cars in otive ve factory produced prod p one day with 168 68 wheels. wheels

2 58

510 people attend a local soccer match. There are 66 more males at the soccer match than females. Find the total otal number of males and females at the soccer match. ch.

Re ga le du ca tio n

1.

Hint: There are more than 250 males at the match.

259

Mrs. Kim bought 5 movie tickets and 4 tubs of popcorn for $84. A tub of popcorn costs half as much as a movie ie ticket. ticke cke Find the cost of each item.

Re ga le du ca tio n

2.

260

In art class, pupils made an equal number of spiders and ants with craft materials. A pipe cleaner was used to make each leg ake eac of the animals. The class used a total of 126 pipe cleaners. aners.

Re ga le du ca tio n

3.

(a) Find the number of each animal made by y the e pupils.

(b) Each ch pupil made 1 animal. How many pupils are in the class?

2 61

Multiples of each coin are selected to give a total amount of $3.09. Twice as many quarters were selected than an pennies. pen Three times as many dimes were selected than nickels. els.

Find the number of each coin selected.

Hint: There are 8 quarters.

Re ga le du ca tio n

4.

2 62

Make a List

Re ga le du ca tio n

Example On vacation, Ethan packed the following clothing items: ems: Tops 1 x T-shirt 1 x singlet

Bottoms 1 x pair of shorts 1 x pair of jeans

wear Footwear 1 x pair pair flip flops 1 x pair pair of runners runne run

How many different ways can Ethan dress ss on vacation? vacatio vacation

T-shirt T-shirt

+ +

shorts orts + flip flip flops fflo shorts horts ts + runners runn

T-shirt T-shirt

+ +

jeans je eans jeans je

singlet et singlet glet

+ +

shorts sho s + flip flops shorts + runners sho

singlet singlet glet

+ +

jeans jean jeans je

+ flip flip flops f + runners ru

+ flip flops + runners

There are 8 different ways Ethan can dress.

2 63

Michelle has forgotten the order of the combination to her bicycle lock. The lock requires 4 digits and she knows ws the he digits d are 2, 5, 6 and 8. Find the maximum number of combinations ombinations binations she must try to find the correct order.

Re ga le du ca tio n

1.

264

Bongo the Clown has 3 hats – pink, yellow and purple.

He also has 3 pairs of shoes – orange, red and blue. e. How ow many different hat and shoe combinations can he e wear? ear?

Re ga le du ca tio n

2.

2 65

Find 10 different ways to make $10 using the coins in the table below.

Re ga le du ca tio n

3.

1

2

3 4

5 6 7

8

9

10

266

Find the sum of the digits from 1 to 20.

Re ga le du ca tio n

4.

5.

How many numberss between etween 100 10 and 200 contain the digit 2?

2 67

Look for Patterns

3 9 5

ed uc ati on

Example ern. Identify dentify the The numbers in each triangle follow the same pattern. pattern and find the missing number.

7

13

27

25 5

6

4

17

5

Let's multiply the numbers att adjacent on the left triangle djacent vertices ver 5 x 3 = 15 3 x 6 = 18 5 x 6 = 30

product are greater than the number Notice that all of the products between the vertices Let's try subtracting the ertices ces of the triangle. ttrian number on the from the product. he opposite vertex ve 15 – 6 = 9 18 – 5 = 13 30 – 3 = 277 We have found the rule and can now find the missing number.

7 x 4 = 28 28 – ? = 25 The missing number is 3.

268

1.

Look for the pattern and fill in the blanks.

3

(b)

3

1

5

5

3

10

2

9

10

110 0

115 5

4

8

Re ga le du ca tio n

(a)

(c)

4

3

27

5

20

(d)

(f)

4

2

12 12

32

50

36

(e)

6

40

40

15

9

180

36

80 80

2 69

The numbers in each triangle follow the same pattern.

Find the missing number.

Re ga le du ca tio n

2.

(a)

8

4

21

6

27 0

6

14

10

3

2

46

4

(b)

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10 58

5

85

50

99

8

9

99

91

9

2 71

Study the numbers in the squares.

Find the missing number.

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3.

(a)

(b)

2

4

3

7

5

6

20

1

10

35

5

9

12

8

3

3

7

2

2

15

27

3

40

9

4

1

7

3

272

5

8

Look for a pattern in the values and answer the questions.

Term

1

2

3

4

5

6

7

Value

8

16

24

32

40

48

56

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4.

(a) What is the value of the 10th term?

h term? rm? (b) What is the value of the 100th

5.

Look for a pattern in the e values and answer the questions.

Term

1

2

3

4

5

6

7

Value

11

22

33 3

44

55

66

77

ev alue of the t 10th term? (a) What is the value

(b) What is th the v value of the 20th term?

2 73

Work Backwards

Re ga

ati on

Example Riley spent 45 minutes eating her lunch. She then attended tended ed her he afternoon classes for 2 and 1/2 hours. After class, she e spent 10 minutes talking with friends. She then took 15 minutes nutes to walk home. She arrived home at 4:05 pm. What time me did Riley start sta eating her lunch?

Let's work backwards the durations. kwards and subtract su 4:05 p.m. m. – 15 min = 3:50 p.m.

3:50 p.m. – 10 min = 3:40 3:4 p.m.

3:40 min = 1:10 p.m.

0 p.m. – 2 hr 30 m 1:10 0 p.m. – 45 min m = 12:25 p.m.

She left school at 3:50 p.m.

She finished classes at 3:40 p.m.

She finished lunch at 1:10 p.m.

She started lunch at 12:25 p.m.

Riley eating her lunch at 12:25 p.m. y started star ea

27 4

Blake visits his father at work. They meet at the office and then take the lift up 12 floors to the observation deck. They ey then hen go down 16 floors to the cafeteria. After that, they take ke the he lift up akes the lift l 7 floors to the fitness center. From there, Blake takes down 21 floors to the ground floor and heads home. me.

On what floor is Blake's dad's office?

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1.

2 75

Keira takes her age in years and multiplies it by 6. She then subtracts 6 and divides by 2. She halves that result and ad adds 5.

Finally she divides that number by 5 and is left with th 4.

Find Keira's age.

Re ga le du ca tio n

2.

2 76

Halle is shopping at the local mall. She buys some guitar strings at the music shop and then goes up 5 floors to the cinema. After the movie, she goes up 3 floors to the he chocolate shop. She then goes down 7 floors to the book shop. The book shop is on level 3. On what level is the music shop? hop? p?

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3.

2 77

tio n

Example boys There are 4 times as many girls playing in the park than boys. e 3 times as 4 more boys arrive at the park, and now there are k in the beginning? beginn begin many girls. How many children were at the park

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y

Before-After Concept

girls

Before

boys

girls

After

boys

4

1 unit = 4

Before e girls: s: 12 units units boys: oys 3 units oys: unit u s

12 x 4 = 48 3 x 4 = 12

48 + 12 = 60

So, there were 60 children at the park in the beginning.

2 78

Jordan had $260 more than Ethan. After Ethan received $80 for his birthday, Jordan had twice as much money as Ethan.

Etha How much money did each person have at first?

Re ga le du ca tio n

1.

2 79

4 years ago, Ella was three times older than her brother Luke.

Today they have a combined age of 20 years. How old d are ar Ella and Luke now?

Re ga le du ca tio n

2.

280

McKenzie has 4 times the number of stickers than Robert.

Robert goes to the store and buys 21 more stickers. They now ey n have an equal number of stickers. How many stickers kerss do they each have?

Re ga le du ca tio n

3.

2 81

Simplify the Problem

ed uc ati on

Example h be e in 40 4 The current month is November. What will the month months?

Let's make a list of the months.

November December January February March April May June July August September October November

– now – 1 month later – 2 months later – 3 months later – 4 months later – 5 months later – 6 months later – 7 months laterr – 8 months later ter – 9 months later – 10 months hs later ater – 11 monthss later ater – 12 months ont later ter

We want to find the month in 40 4 month's time.

Let's divide by 12 and nd match the remainder to the months above.

40 ÷ 12 = 3 R 4 There iss a remainder of 4, so the 40th month after November mberr is March.

Marc

282

Today is Monday, what day will it be in 45 days?

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1.

2.

Today is Wednesday, y, what day will w it be in 288 days?

2 83

The current month is February. What month will it be in 175 month's time?

Re ga le du ca tio n

3.

4.

Look at the repeating pattern tern ern of 5 shapes. shap shape

...

nti , what will w the 12th shape be? What will If the pattern continues, e be? the 184th shape

284